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BEGIN:VEVENT
SUMMARY:Bhargav Bhatt (University of Michigan)
DTSTART:20200618T160000Z
DTEND:20200618T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/1
DESCRIPTION:Title: A p-adic Riemann-Hilbert functor and applications\nby Bhargav B
hatt (University of Michigan) as part of Recent Advances in Modern p-Adic
Geometry (RAMpAGe)\n\n\nAbstract\nI will discuss an ongoing project (joint
with Jacob Lurie) aiming to construct a p-adic Riemann-Hilbert functor\,
attaching coherent objects to constructible sheaves (with coefficients in
F_p\, Z_p or Q_p) on a compact algebraic variety over a p-adic field. I'll
focus on the case of F_p-coefficients\, which leads to a solution of some
old questions in commutative algebra.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Howe (University of Utah)
DTSTART:20200625T160000Z
DTEND:20200625T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/2
DESCRIPTION:Title: A p-adic transcendence criterion for CM Galois representations\
nby Sean Howe (University of Utah) as part of Recent Advances in Modern p-
Adic Geometry (RAMpAGe)\n\n\nAbstract\nWe show that a crystalline Galois r
epresentation with rational de Rham lattice admits a slope filtration with
abelian isoclinic subquotients. As a corollary\, we find that a $p$-divis
ible group over $\\mathcal{O}_{\\mathbb{C_p}}$ has complex multiplication
if and only if it can be defined over a complete discretely valued subfiel
d and its Hodge-Tate filtration is algebraic -- this is a $p$-adic analog
of classical transcendence results for complex abelian varieties due to Sc
hneider\, Cohen\, and Shiga-Wolfart. More generally\, we characterize the
special points of the diamond moduli of mixed-characteristic local shtuka
with one paw as those with algebraic Hodge-Tate and de Rham periods. The c
orresponding archimedean transcendence results for Shimura varieties fit i
nto a broader framework of bialgebraicity that plays an important role in
the Andre-Oort conjecture\, and\, time permitting\, we discuss some ideas
of what this might look like in the $p$-adic setting.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Scholze (University of Bonn / MPIM)
DTSTART:20200716T160000Z
DTEND:20200716T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/3
DESCRIPTION:Title: Prismatic crystals and crystalline Galois representations\nby P
eter Scholze (University of Bonn / MPIM) as part of Recent Advances in Mod
ern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nLet $K$ be a complete discret
e valuation field of mixed\ncharacteristic with perfect residue field. We
prove that F-crystals on\nthe prismatic site of $\\mathcal{O}_K$ are equiv
alent to lattices in crystalline\n$G_K$-representations. (joint with Bharg
av Bhatt)\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wiesława Nizioł (Sorbonne / IMJ)
DTSTART:20200730T160000Z
DTEND:20200730T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/4
DESCRIPTION:Title: p-adic étale cohomology of period domains\nby Wiesława Nizio
ł (Sorbonne / IMJ) as part of Recent Advances in Modern p-Adic Geometry (
RAMpAGe)\n\n\nAbstract\nI will show how to compute $p$-adic étale cohomol
ogy with compact support of period domains over local fields in the case o
f a basic isocrystal for quasi-split reductive groups. This follow the met
hod used by Orlik in his computations of the $\\ell$-adic étale cohomolog
y using as a key new input the computation of Ext groups between mod-$p$ g
eneralized Steinberg representations of $p$-adic groups. This is a joint w
ork with Colmez\, Dospinescu\, and Hauseux.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shizhang Li (University of Michigan)
DTSTART:20200702T160000Z
DTEND:20200702T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/5
DESCRIPTION:Title: Some examples and results on integral p-adic Hodge filtrations\
nby Shizhang Li (University of Michigan) as part of Recent Advances in Mod
ern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nGiven a smooth proper scheme
over a mixed characteristic DVR\, we try to understand to what extent the
special fiber knows the Hodge numbers of the generic fiber. I'll provide s
ome examples as well as a theorem showing that in "good" situations some n
umbers defined purely using the special fiber actually give the Hodge numb
ers of the generic fiber. This naturally leads to consideration of Breuil-
Kisin prismatic cohomology\, and I'll describe an example which illustrate
s certain pathological behavior of Hodge-Tate and Hodge-de Rham spectral s
equences in mixed characteristic situations.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan Zavyalov (Stanford)
DTSTART:20200723T170000Z
DTEND:20200723T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/6
DESCRIPTION:Title: Mod-p Poincaré duality in p-adic geometry\nby Bogdan Zavyalov
(Stanford) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\
n\n\nAbstract\nÉtale cohomology of $\\mathbf{F}_p$-local systems does no
t behave nicely on general smooth p-adic rigid-analytic spaces\; e.g.\, th
e $\\mathbf{F}_p$-cohomology of the 1-dimensional closed unit ball is infi
nite. However\, it turns out that things are much better for proper p-adic
rigid-analytic spaces. For example\, Scholze used perfectoid spaces to sh
ow that proper p-adic rigid-analytic spaces have finite cohomology for any
$\\mathbf{F}_p$-local system. Based on Gabber's idea\, I will introduce t
he concept of almost coherent sheaves and use it to “localize” (in an
appropriate sense) some problems in the étale cohomology of rigid-analyti
c spaces. For example\, this theory (together with perfectoid spaces) can
be used to give a "new" proof of the finiteness theorem and a proof of Poi
ncaré duality for p-torsion coefficients on smooth and proper p-adic rigi
d-analytic spaces.\n\nThis is work in progress.\n\nPlease note that this t
alk begins one hour later than the usual time.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Imperial)
DTSTART:20200806T160000Z
DTEND:20200806T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/7
DESCRIPTION:Title: A comparison theorem for ordinary p-adic modular forms\nby Ana
Caraiani (Imperial) as part of Recent Advances in Modern p-Adic Geometry (
RAMpAGe)\n\n\nAbstract\nI will discuss joint work in progress with Elena M
antovan and James Newton\, whose goal is to compare ordinary completed coh
omology with (higher) Hida theory\, in the special case of the modular cur
ve. Both these notions go back to Hida\, though the former can be reinterp
reted using Emerton’s functor of ordinary parts applied to completed coh
omology\, and the latter has been redeveloped and expanded recently by Box
er and Pilloni to incorporate higher coherent cohomology. Our work gives a
new proof to a theorem of Ohta\, that is perhaps more amenable to general
isation. The key ingredients are the Bruhat stratification on the Hodge-Ta
te period domain\, and the integral comparison results pioneered by Bhatt\
, Morrow and Scholze.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Chan (MIT)
DTSTART:20200709T160000Z
DTEND:20200709T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/8
DESCRIPTION:Title: L-packets of S-unramified regular supercuspidal representations
\nby Charlotte Chan (MIT) as part of Recent Advances in Modern p-Adic Geom
etry (RAMpAGe)\n\n\nAbstract\nIn 2001\, Yu gave an algebraic construction
of supercuspidal\nrepresentations of p-adic groups (now known to be exhaus
tive when the\nresidual characteristic is sufficiently large---Kim\, Fintz
en). There\nhas since been a lot of progress towards explicitly constructi
ng the\nlocal Langlands correspondence: Kazhdan-Varshavsky and DeBacker-Re
eder\n(depth zero)\, Reeder and DeBacker-Spice (unramified toral)\, and\nK
aletha (regular supercuspidals). In this talk\, we present recent and\nong
oing work investigating a geometric counterpart to this story. This\nis ba
sed on joint work with Alexander Ivanov and joint work with Masao\nOi.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Magner (Boston University)
DTSTART:20200813T160000Z
DTEND:20200813T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/9
DESCRIPTION:Title: On the Cohomology of Moduli of Mixed Characteristic Shtukas\nby
Richard Magner (Boston University) as part of Recent Advances in Modern p
-Adic Geometry (RAMpAGe)\n\n\nAbstract\nWe review mixed characteristic sht
ukas and their moduli. These generalize the Lubin-Tate tower and other Rap
oport-Zink spaces. Under the Kottwitz conjecture\, the cohomology of thes
e spaces are expected to realize the local Langlands correspondence. The
data defining these spaces involve cocharacters of a Lie group\; when the
cocharacter is minuscule\, we recover classical Rapoport-Zink spaces. In
the case of $\\mathrm{GL}_n$\, we show that the Kottwitz conjecture for g
eneral cocharacters can be reduced to the minuscule case. This depends on
a geometric Satake equivalence for the $B_{\\mathrm{dR}}$-affine Grassman
ian\, due to Fargues and Scholze\, and a formula of Imai on cohomology der
ived from it.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Cass (Harvard University)
DTSTART:20200820T160000Z
DTEND:20200820T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/10
DESCRIPTION:Title: Mod p Hecke algebras and perverse F_p-sheaves\nby Robert Cass
(Harvard University) as part of Recent Advances in Modern p-Adic Geometry
(RAMpAGe)\n\n\nAbstract\nWe explain a mod $p$ version of the geometric Sat
ake isomorphism which gives a sheaf-theoretic description of the spherical
mod $p$ Hecke algebra. We also construct central elements in the Iwahori
mod p Hecke algebra by adapting a method due to Gaitsgory. Our proofs rely
crucially on the theory of $F$-singularities\, and along the way we prove
new results about the singularities of affine Schubert varieties. We expe
ct these results to have applications toward a mod $p$ Langlands correspon
dence.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miaofen Chen (East China Normal University)
DTSTART:20200910T150000Z
DTEND:20200910T162000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/12
DESCRIPTION:Title: Connectedness of Kisin varieties associated to absolutely irreduc
ible Galois representations\nby Miaofen Chen (East China Normal Univer
sity) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\n
Abstract\nAbstract: Let $K$ be a $p$-adic field. Let $\\rho$ be an $n$-dim
ensional continuous absolutely irreducible mod $p$ representation of the a
bsolute Galois group of $K$. The Kisin variety is a projective scheme whic
h parametrizes the finite flat group schemes over the ring of integers of
$K$ with generic fiber $\\rho$ satisfying some determinant condition. The
connected components of the Kisin variety is in bijection with the connect
ed components of the generic fiber of the flat deformation ring of $\\rho$
with given Hodge-Tate weights. Kisin conjectured that the Kisin variety
is connected in this case. We show that Kisin's conjecture holds if $K$ i
s totally ramified with $n=3$ or the determinant condition is of a very pa
rticular form. We also give counterexamples to show Kisin's conjecture do
es not hold in general. This is a joint work with Sian Nie.\n\nPlease note
that this talk is one hour earlier than usual.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Gleason (Berkeley)
DTSTART:20201001T160000Z
DTEND:20201001T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/13
DESCRIPTION:Title: On the geometric connected components of moduli of mixed character
istic shtukas\nby Ian Gleason (Berkeley) as part of Recent Advances in
Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nBy a theorem of Scholze a
nd Weinstein\, moduli spaces of mixed characteristic shtukas generalize Ra
poport-Zink spaces at infinite level. In this talk\, we describe the struc
ture of the set of geometric connected components of those moduli spaces t
hat are associated to the data $(G\,b\,\\mu)$ with $G$ an unramified reduc
tive group and $(b\,\\mu)$ HN-irreducible. This result generalizes the wor
k of Chen on the geometric connected components of unramified HN-irreducib
le Rapoport-Zink spaces of EL and PEL type. In the interest of time\, we o
nly sketch the part of the proof that requires a new geometric ingredient:
namely\, the specialization map for Scholze's category of diamonds.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lue Pan (University of Chicago)
DTSTART:20200827T160000Z
DTEND:20200827T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/14
DESCRIPTION:Title: On the locally analytic vectors of the completed cohomology of mod
ular curves\nby Lue Pan (University of Chicago) as part of Recent Adva
nces in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nWe study locally a
nalytic vectors of the completed cohomology of\nmodular curves and determi
ne eigenvectors of a rational Borel subalgebra\nof gl_2(Q_p). As applicati
ons\, we are able to prove a classicality result\nfor overconvergent eigen
form of weight one and give a new proof of\nFontaine-Mazur conjecture in t
he irregular case under some mild\nhypothesis. One technical tool is relat
ive Sen theory which allows us to\nrelate infinitesimal group action with
Hodge(-Tate) structure.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Wear (Utah)
DTSTART:20201008T160000Z
DTEND:20201008T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/15
DESCRIPTION:Title: Perfectoid covers of abelian varieties and the weight-monodromy co
njecture\nby Peter Wear (Utah) as part of Recent Advances in Modern p-
Adic Geometry (RAMpAGe)\n\n\nAbstract\nDeligne's weight-monodromy conjectu
re gives control over the zeros of local factors of L-functions of varieti
es at places of bad reduction. His proof in characteristic p was a step in
his proof of the generalized Weil conjectures. Scholze developed the theo
ry of perfectoid spaces to transfer Deligne's proof to characteristic 0\,
proving the conjecture for complete intersections in toric varieties. Buil
ding on Scholze's techniques\, we prove the weight-monodromy conjecture fo
r complete intersections in abelian varieties. Part of this talk will disc
uss joint work with Blakestad\, Gvirtz\, Heuer\, Shchedrina\, Shimizu\, an
d Yao.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Viehmann (TU Munchen)
DTSTART:20200917T160000Z
DTEND:20200917T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/16
DESCRIPTION:Title: Newton strata in the weakly admissible locus\nby Eva Viehmann
(TU Munchen) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe
)\n\n\nAbstract\nGiven a reductive group G over a p-adic local field and a
minuscule\ncocharacter\, Rapoport and Zink constructed an open subspace i
nside the\nassociated adic flag variety\, called p-adic period domain or w
eakly\nadmissible locus. These are vast generalizations of Drinfeld upper
half\nspaces. Recently\, Caraiani and Scholze defined a Newton stratificat
ion\non adic flag varieties. The unique open Newton stratum coincides with
\nthe so-called admissible locus\, and is contained in the weakly\nadmissi
ble locus. However\, in most cases the two spaces do not coincide.\nIn my
talk\, I describe which of the other Newton strata intersect the\nweakly a
dmissible locus.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dustin Clausen (Copenhagen)
DTSTART:20200924T160000Z
DTEND:20200924T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/17
DESCRIPTION:Title: Quasicoherent sheaves on rigid analytic spaces\nby Dustin Clau
sen (Copenhagen) as part of Recent Advances in Modern p-Adic Geometry (RAM
pAGe)\n\n\nAbstract\nI will describe a theory of "solid" quasicoherent she
aves on rigid analytic spaces\, and explain how its basic properties give
conceptually simple proofs of various foundational results concerning vect
or bundles and coherent sheaves in rigid geometry. This is joint work wit
h Peter Scholze.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:*No meeting*
DTSTART:20200903T160000Z
DTEND:20200903T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/18
DESCRIPTION:by *No meeting* as part of Recent Advances in Modern p-Adic Ge
ometry (RAMpAGe)\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haoyang Guo (Michigan)
DTSTART:20201015T160000Z
DTEND:20201015T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/19
DESCRIPTION:Title: Hodge-Tate decomposition for non-smooth rigid spaces\nby Haoya
ng Guo (Michigan) as part of Recent Advances in Modern p-Adic Geometry (RA
MpAGe)\n\n\nAbstract\nGiven a smooth projective variety over a $p$-adic fi
eld\, its $p$-adic étale cohomology admits a natural Galois equivariant d
ecomposition\, called Hodge-Tate decomposition. The decomposition builds a
connection between the underlying $p$-adic Galois representation and the
cohomology of differentials\, relating arithmetic and geometric informatio
n altogether. In this talk\, we generalize Hodge-Tate decomposition to non
-smooth rigid spaces\, and show how to compute $p$-adic étale cohomology
via cohomology of Deligne-Du Bois complexes.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cong Xue (Cambridge)
DTSTART:20201105T170000Z
DTEND:20201105T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/20
DESCRIPTION:Title: Smoothness of the cohomology sheaves of stacks of shtukas\nby
Cong Xue (Cambridge) as part of Recent Advances in Modern p-Adic Geometry
(RAMpAGe)\n\n\nAbstract\nLet $X$ be a smooth projective geometrically conn
ected curve\nover a finite field $\\mathbb{F}_q$. Let $G$ be a connected r
eductive group over the\nfunction field of $X$. For every finite set $I$ a
nd every representation of\n$(\\check{G})^I$\, where $\\check{G}$ is the L
anglands dual group of $G$\, we have\na stack of shtukas over $X^I$. For e
very degree\, we have a compact support\nl-adic cohomology sheaf over $X^I
$.\n\nIn this talk\, I will recall some properties of these sheaves. I wil
l\ntalk about a work in progress which proves that these sheaves are\nind-
smooth over $X^I$.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Achinger (IMPAN Warsaw)
DTSTART:20201022T160000Z
DTEND:20201022T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/21
DESCRIPTION:Title: Hodge theory over $\\mathbf{C}((t))$\nby Piotr Achinger (IMPAN
Warsaw) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\
n\nAbstract\nI will describe some ways in which Hodge theory makes its way
into the\ngeometry of rigid-analytic varieties over $\\mathbf{C}((t))$. N
amely\, such spaces\nhave a "Betti realization"\, well-defined up to homot
opy (joint work\nwith Talpo)\, and their cohomology carries a mixed Hodge
Structure\n(Steenbrink\, Stewart-Vologodsky\, Berkovich). The notion of "p
rojective\nreduction" introduced by Li and studied by Hansen-Li is a good
working\nanalog of the Kaehler condition. In this case\, Hodge symmetry ho
lds\,\neven though it fails in some cases over the $p$-adic numbers (Petro
v).\nMoreover\, there is a Riemann-Hilbert correspondence (work in\nprogre
ss)\, which should allow us to define variations of mixed Hodge\nstructure
in this context. All of these analogs rely on corresponding\nstatements r
egarding the logarithmic special fiber of a semistable\nmodel. Open proble
ms abound.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Reinecke (IAS)
DTSTART:20201119T170000Z
DTEND:20201119T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/22
DESCRIPTION:Title: The cohomology of moduli of curves at infinite level\nby Emanu
el Reinecke (IAS) as part of Recent Advances in Modern p-Adic Geometry (RA
MpAGe)\n\n\nAbstract\nBy work of Harer\, the Betti cohomology of the modul
i space of smooth\, complex curves of genus $g > 1$ vanishes in degrees ab
ove $4g - 5$. In my talk\, I give a new perspective on this result which u
ses $p$-adic geometry. The approach also yields statements about moduli of
stable curves and curves of compact type that are not covered by Harer's
methods.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linus Hamann (Princeton)
DTSTART:20201029T160000Z
DTEND:20201029T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/23
DESCRIPTION:Title: Compatibility of the Fargues-Scholze and Gan-Takeda Local Langland
s Correspondences\nby Linus Hamann (Princeton) as part of Recent Advan
ces in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nIn upcoming work\,
Fargues and Scholze construct a candidate for a general local Langlands co
rrespondence\, \nassociating to a smooth irreducible representation of a
connected reductive group $G/\\mathbf{Q}_{p}$ a continuous semisimple Weil
parameter\, using the action of excursion operators\non the moduli space
of $G$-bundles on the Fargues-Fontaine curve. It is a natural question to
ask whether this correspondence is compatible with known instances of the
local Langlands correspondence after semi-simplification. For $G = \\mathr
m{GL}_{n}$\, this compatibility is deduced from the fact that corresponden
ce of Harris-Taylor is realized in the cohomology of the Lubin-Tate tower
at infinite level\, via its interpretation as a moduli space of mixed char
acteristic shtukas. For $G = \\mathrm{GSp}_{4}$ or its inner form $\\mathr
m{GU}_{2}(D)$\, there is a local Langlands correspondence constructed by G
an-Takeda and Gan-Tantono\, respectively. We will discuss upcoming work re
lated to proving compatibility in this case. Similar to the case of $\\mat
hrm{GL}_{n}$\, this involves realizing this local Langlands correspondence
in the cohomology of the local Shimura varieties at infinite level associ
ated with these groups. We do this by applying basic uniformization of the
se local Shimura varieties due to Shen\, as well as results on Galois repr
esentations in the cohomology of the relevant global Shimura varieties due
to Sorensen and Kret-Shin. After proving this compatibility\, we employ v
arious new ideas from the geometry of the Fargues Scholze correspondence t
o obtain a complete description of the $\\rho$-isotypic part of the cohomo
logy of this local Shimura variety at infinite level\, where $\\rho$ is a
representation of $G$ with supercuspidal Gan-Takeda or Gan-Tantono paramet
er\, thereby verifying the strongest form of the Kottwitz conjecture for t
hese specific representations.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiran Kedlaya (UCSD)
DTSTART:20201112T170000Z
DTEND:20201112T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/24
DESCRIPTION:Title: Several forms of Drinfeld's lemma\nby Kiran Kedlaya (UCSD) as
part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\
nThe term "Drinfeld's lemma" refers to several related statements about\nt
he behavior of etale fundamental groups under formation of products in\nmi
xed or positive characteristic. We discuss statements of this form in\nthe
contexts of schemes (after Drinfeld and Lau)\, perfectoid spaces (after\n
Scholze-Weinstein\, Carter-Kedlaya-Zabradi\, and Fargues-Scholze)\, and\nF
-isocrystals (work in progress).\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Newton (King's College London)
DTSTART:20201203T170000Z
DTEND:20201203T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/25
DESCRIPTION:Title: Symmetric power functoriality and the geometry of eigenvarieties\nby James Newton (King's College London) as part of Recent Advances in
Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nI will discuss work with J
ack Thorne on symmetric power functoriality for modular forms\, with a foc
us on the role of eigenvarieties and their geometry.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (MIT/IAS)
DTSTART:20201210T170000Z
DTEND:20201210T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/26
DESCRIPTION:Title: Equivariant localization\, parity sheaves\, and cyclic base change
\nby Tony Feng (MIT/IAS) as part of Recent Advances in Modern p-Adic G
eometry (RAMpAGe)\n\n\nAbstract\nLafforgue and Genestier-Lafforgue have
constructed the global and (semisimplified) local Langlands correspondenc
es for arbitrary reductive groups over function fields. I will explain so
me recently established properties of these correspondences regarding base
change functoriality: existence of transfers for mod $p$ automorphic form
s through $p$-cyclic base change in the global correspondence\, and Tate c
ohomology realizes $p$-cyclic base change in the mod $p$ local corresponde
nce. In particular\, the local statement verifies a conjecture\nof Treuman
n-Venkatesh. The proofs combine Lafforgue’s theory with equivariant loca
lization arguments for shtukas as well as recent advances in modular repre
sentation theory\, namely parity sheaves and Smith-Treumann theory. Compar
ed with previous iterations of the talk\,\nthis time the talk will emphasi
ze the role of the new representation-theoretic tools\, during the extra 2
0 minutes.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lynnelle Ye (Stanford)
DTSTART:20201217T170000Z
DTEND:20201217T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/27
DESCRIPTION:Title: The valuative criterion for properness for eigenvarieties\nby
Lynnelle Ye (Stanford) as part of Recent Advances in Modern p-Adic Geometr
y (RAMpAGe)\n\n\nAbstract\nThe question of whether the Coleman-Mazur eigen
curve satisfies the valuative criterion for properness was first asked by
Coleman and Mazur in 1998 and settled by Diao and Liu in 2016 using deep\,
powerful Galois-theoretic machinery. We will discuss a new proof which is
short and explicit and uses no Galois theory. Instead we adapt an earlier
method of Buzzard and Calegari based on elementary properties of overconv
ergent modular forms\, for which we have to extend Pilloni's geometric con
struction of overconvergent forms of arbitrary weight farther into the sup
ersingular locus. We will also discuss generalizations in progress.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Ivanov (Universitat Bonn)
DTSTART:20210107T170000Z
DTEND:20210107T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/28
DESCRIPTION:Title: On $p$-adic Deligne--Lusztig spaces\nby Alexander Ivanov (Univ
ersitat Bonn) as part of Recent Advances in Modern p-Adic Geometry (RAMpAG
e)\n\n\nAbstract\nWe discuss a new definition of $p$-adic Deligne--Lusztig
spaces\,\nas arc-sheaves on perfect algebras over the residue field. We l
ook then\nat some fundamental properties of these sheaves. In particular\,
we show\nthat they are ind-representable in many cases. Along the way we
discuss\na general result saying that the (perfect) loop space of a\nquasi
-projective scheme over $\\mathbf{Q}_p$ is an arc-sheaf.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebecca Bellovin
DTSTART:20210114T180000Z
DTEND:20210114T192000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/29
DESCRIPTION:Title: Galois representations over pseudorigid spaces\nby Rebecca Bel
lovin as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\n
Abstract\nIn the past few years\, extended eigenvarieties with\n"boundary"
in positive characteristic have been constructed as\n"pseudorigid spaces"
. I will discuss the construction of\n$(\\varphi\,\\Gamma)$-modules for $
p$-adic Galois representations with\ncoefficients in pseudoaffinoid algebr
as and discuss some of their\nproperties. I will conclude by giving appli
cations to the extended\neigencurve at the boundary of weight space.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Dospinescu (ENS Lyon)
DTSTART:20210121T170000Z
DTEND:20210121T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/30
DESCRIPTION:Title: Cohomology of the Drinfeld tower: a family affair\nby Gabriel
Dospinescu (ENS Lyon) as part of Recent Advances in Modern p-Adic Geometry
(RAMpAGe)\n\n\nAbstract\nI will report on joint work with Pierre Colmez a
nd Wieslawa\nNiziol\, refining our previous results on the cohomology of t
he coverings\nof the Drinfeld half-space for GL_2(Q_p). Here we deal with
integral and\n“family" aspects of the cohomology\, as well as the realis
ation of the\np-adic local Langlands correspondence for GL_2(Q_p) for all\
ntwo-dimensional representations of the absolute Galois group of Q_p. A\nk
ey role is played by a re-interpretation of Scholze’s functor.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Heuer (Universitat Bonn)
DTSTART:20210128T170000Z
DTEND:20210128T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/31
DESCRIPTION:Title: v-vector bundles on rigid spaces\nby Ben Heuer (Universitat Bo
nn) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAb
stract\nThis talk is about the difference between vector bundles on a\nsmo
oth rigid space X and v-vector bundles on the associated diamond. In\nthe
case of line bundles\, I will explain how this difference can be\nfully de
scribed in terms of differentials using a "Hodge-Tate logarithm"\nmap. For
proper X\, I will explain how one can use the proétale universal\ncover
of X to interpret this description as a p-adic Simpson\ncorrespondence of
rank 1.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Yun Hsu (UCLA)
DTSTART:20210318T150000Z
DTEND:20210318T162000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/32
DESCRIPTION:Title: Partial classicality of Hilbert modular forms\nby Chi-Yun Hsu
(UCLA) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\
nAbstract\nLet $p$ be an inert prime in a totally real field $F$ for simpl
icity. Using the method of analytic continuation\, Kassaei proved a classi
cality theorem: an overconvergent Hilbert $U_p$-eigenform is automatically
classical when the slope is small compared to the weights. In analogy to
overconvergent forms\, which are defined over a strict neighborhood of the
zero locus of the Hasse invariant\, one can define partially classical ov
erconvergent forms as defined over a strict neighborhood of the zero locus
of a sub-collection of partial Hasse invariants. Under a weaker small slo
pe condition depending on the relevant weights\, we show that an overconve
rgent $U_p$-eigenform is partially classical.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Petrov (Harvard)
DTSTART:20210304T160000Z
DTEND:20210304T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/33
DESCRIPTION:Title: Geometrically irreducible $p$-adic local systems are de Rham up to
a twist\nby Alexander Petrov (Harvard) as part of Recent Advances in
Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nLet $K$ be a p-adic field.
Although there are plenty of non-de Rham representations of the Galois gr
oup of $K$\, it turns out that for any smooth variety $X$ over $K$ and a $
\\overline{\\mathbf{Q}}_p$-local system $L$ on $X$ such that the restricti
on of $L$ to $X_{\\overline{K}}$ is irreducible\, there exists a character
of the Galois group of $K$ such that twisting by this character turns $L$
into a de Rham local system. In particular\, for a geometrically irreduci
ble $\\overline{\\mathbf{Q}}_p$-local system on a smooth variety over a nu
mber field\, the associated projective representation of the fundamental g
roup automatically satisfies the assumptions of the relative Fontaine-Mazu
r conjecture.\n\nThe proof uses $p$-adic Riemann-Hilbert correspondence in
the form constructed by Liu and Zhu as well as its logarithmic version co
nstructed by Diao-Lan-Liu-Zhu and their decompletions developed by Shimizu
.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Kramer-Miller (UC Irvine)
DTSTART:20210211T170000Z
DTEND:20210211T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/34
DESCRIPTION:Title: The ramification of p-adic representations coming from geometry\nby Joe Kramer-Miller (UC Irvine) as part of Recent Advances in Modern p
-Adic Geometry (RAMpAGe)\n\n\nAbstract\nThe purpose of this talk is to exp
lain a geometric analogue of Sen's classical theorem\, which describes the
close relationship between $p$-adic Lie filtrations and ramification filt
rations for $p$-adic fields. Let $X$ be a smooth variety over a perfect fi
eld $k$ with characteristic $p>0$\, let $D\\subset X$ be a reduced divisor
with smooth normal crossings\, and let $U=X\\backslash D$. Consider a con
tinuous representation $\\rho:\\pi_1(U) \\to GL(\\Z_p)$\, which gives rise
to an $p$-adic Lie tower of \\'etale covers $U_n \\to U$. We may associat
e to each cover a Swan divisor $sw(U_n/U)$\, supported on $D$\, using the
ramification filtration of Abbes-Saito. In general\, the growth of these d
ivisors can be arbitrarily wild. Instead\, we restrict ourselves to repres
entations that are ordinary geometric (e.g. $\\rho$ arises as the $p$-adic
Tate module of a family of ordinary Abelian varieties). Our main result s
tates that for $\\rho$ ordinary geometric\, there exists integers $c_1>c_0
>0$ such that $c_1p^{2n} D > sw(U_n/U) > c_0 p^{2n}D$. This says that even
though $\\rho$ has infinite monodromy\, the Swan conductors $sw(U_n/U)$ g
row as `slowly as possible'.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Fox (Oregon)
DTSTART:20210225T170000Z
DTEND:20210225T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/35
DESCRIPTION:Title: Supersingular loci of some unitary Shimura varieties\nby Maria
Fox (Oregon) as part of Recent Advances in Modern p-Adic Geometry (RAMpAG
e)\n\n\nAbstract\nUnitary Shimura varieties are moduli spaces of abelian v
arieties with an action of a quadratic imaginary field\, and extra structu
re. In this talk\, we'll discuss specific examples of unitary Shimura vari
eties whose supersingular loci can be concretely described in terms of Del
igne-Lusztig varieties. By Rapoport-Zink uniformization\, much of the stru
cture of these supersingular loci can be understood by studying an associa
ted moduli space of p-divisible groups (a Rapoport-Zink space). We'll disc
uss the geometric structure of these associated Rapoport-Zink spaces as we
ll as some techniques for studying them.\n\n**Note from the organizers: S
tarting on March 4\, the seminar will be moving one hour earlier\, to 11:0
0 Boston / 17:00 Paris. This change does not apply to the talk on March 1
1\, which is still at 12:00 Boston / 18:00 Paris. We apologize for any in
convenience.**\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Judith Ludwig (Heidelberg)
DTSTART:20210408T150000Z
DTEND:20210408T162000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/36
DESCRIPTION:Title: Endoscopic points on the SL(2)-eigencurve\nby Judith Ludwig (H
eidelberg) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\
n\n\nAbstract\nAfter recalling some background on Langlands correspondence
s and $L$-packets for $\\mathrm{SL}(2)$\, we will study endoscopy in the s
etting of eigenvarietes. I will explain the existence of some interesting
$p$-adic automorphic forms that can be seen using the $\\mathrm{SL}(2)$-ei
gencurve at certain endoscopic points. Finally I will report on work in p
rogress with C. Johansson\, where we study the $\\mathrm{SL}(2)$-eigencurv
e at endoscopic points via the Coleman-Mazur eigencurve.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Mann (Bonn)
DTSTART:20210218T170000Z
DTEND:20210218T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/37
DESCRIPTION:Title: $p$-adic six functors on diamonds\nby Lucas Mann (Bonn) as par
t of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nMo
tivated by $p$-adic Poincaré duality in rigid geometry\, we develop a $p$
-adic six functor formalism on rigid varieties\, or more generally for dia
monds. This is achieved by defining a category of "quasi-coherent $\\mathc
al{O}_X^+/p$-modules" on a diamond $X$ and then using the recent developme
nt of a quasi-coherent 6-functor formalism on schemes by Clausen-Scholze t
o obtain a similar 6-functor formalism on diamonds. One easily deduces the
desired p-adic Poincaré duality on a smooth proper rigid variety $X$ in
mixed characteristic\, noting that by Scholze's primitive comparison theor
em\, $\\mathbb F_p$-cohomology on $X$ can be computed via cohomology of th
e sheaf $O_X^+/p$. Of course\, our p-adic 6-functor formalism allows for m
any more potential applications\; for example\, we expect to gain new insi
ghts in the $p$-adic Langlands program.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroki Kato (Paris Saclay)
DTSTART:20210311T170000Z
DTEND:20210311T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/38
DESCRIPTION:Title: Etale cohomology of algebraizable rigid analytic varieties via nea
rby cycles over general bases\nby Hiroki Kato (Paris Saclay) as part o
f Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nOne o
f the most fundamental results in the study of étale cohomology of rigid
analytic varieties is the comparison with the nearby cycle cohomology\, wh
ich gives a canonical isomorphism between the cohomology of an algebraizab
le rigid analytic variety and the cohomology of the nearby cycle. \nI will
discuss a generalization of this comparison result to the relative case:
For an algebraizable morphism\, the compactly supported higher direct imag
e sheaves are identified\, up to replacing the target by a blowup\, with a
generalization of the nearby cycle cohomology\, which is given by the the
ory of nearby cycles over general bases. \nThis result can be used to show
the existence of a tubular neighborhood that doesn’t change the cohomol
ogy for algebraizable families.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guido Bosco (IMJ)
DTSTART:20210617T160000Z
DTEND:20210617T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/40
DESCRIPTION:Title: Rational p-adic Hodge theory for non-proper rigid-analytic varieti
es\nby Guido Bosco (IMJ) as part of Recent Advances in Modern p-Adic G
eometry (RAMpAGe)\n\n\nAbstract\nThe goal of this talk will be to discuss
the rational p-adic Hodge\ntheory of general smooth rigid-analytic varieti
es. The study of this\nsubject for varieties that are not necessarily prop
er (e.g. Stein) is\nmotivated in part by the desire of finding a geometric
incarnation of\nthe p-adic Langlands correspondence in the cohomology of
local Shimura\nvarieties. In this context\, one difficulty is that the rel
evant\ncohomology groups (such as the p-adic (pro-)étale\, and de Rham on
es) are\nusually infinite-dimensional\, and\, to study them\, it becomes i
mportant\nto exploit the topological structure that they carry. But\, in d
oing so\,\none quickly runs into several topological issues: for example\,
the de\nRham cohomology groups of a smooth affinoid space are\, in genera
l\, not\nHausdorff. We will explain how to overcome these issues\, using t
he\ncondensed and solid formalisms recently developed by Clausen and\nScho
lze\, and we will report on a comparison theorem describing the\ngeometric
p-adic (pro-)étale cohomology in terms of de Rham data\, for a\nlarge cl
ass of smooth rigid-analytic varieties defined over a p-adic\nfield. In pa
rticular\, we recover results of Colmez\, Dospinescu\, and\nNizioł.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hélène Esnault (FU Berlin)
DTSTART:20210415T150000Z
DTEND:20210415T162000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/41
DESCRIPTION:Title: Connections and Symmetric Differential Forms\nby Hélène Esna
ult (FU Berlin) as part of Recent Advances in Modern p-Adic Geometry (RAMp
AGe)\n\n\nAbstract\n(work in progress with Michael Groechenig)\nIf $X$ is
smooth complex projective and does not have any non-trivial symmetric diff
erential forms\, then all its complex local systems have finite monodromy
(Brunebarbe-Klingler-Totaro ’13\, in answer to a question I had posed).
The proof relies on positivity theory stemming from Hodge Theory.\n\nThe a
im is to understand a suitable formulation in characteristic $p>0$.\n\nIf
$X$ is smooth projective over the algebraic closure $k$ of finite field\
, and does not have non-trivial differential forms\, one may ask whether a
ll convergent isocrystals have finite monodromy. This is true if $X$ lifts
to $W(k)$. If $X$ lifts to $W_2(k)$\, one can show that stable rank $2$
connections of degree $0$ have finite monodromy (i.e. are trivializable by
a finite étale cover).\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Dotto (Chicago)
DTSTART:20210422T150000Z
DTEND:20210422T162000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/42
DESCRIPTION:Title: Mod p Bernstein centres of p-adic groups\nby Andrea Dotto (Chi
cago) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\n
Abstract\nThe centre of the category of smooth mod p representations of a
p-adic reductive group does not distinguish the blocks of finite length re
presentations\, in contrast with Bernstein's theory in characteristic zero
. Motivated by this observation and the known connections between the Bern
stein centre and the local Langlands correspondence in families\, we consi
der the case of GL_2(Q_p) and we prove that its category of representation
s extends to a stack on the Zariski site of a simple geometric object: a c
hain X of projective lines\, whose points are in bijection with Paskunas's
blocks. Taking the centre over each open subset we obtain a sheaf of ring
s on X\, and we expect the resulting space to be closely related to the Em
erton--Gee stack for 2-dimensional representations of the absolute Galois
group of Q_p. Joint work in progress with Matthew Emerton and Toby Gee.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timo Richarz (Darmstadt)
DTSTART:20210506T150000Z
DTEND:20210506T162000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/43
DESCRIPTION:Title: A categorical Kunneth formula for Weil sheaves\nby Timo Richar
z (Darmstadt) as part of Recent Advances in Modern p-Adic Geometry (RAMpAG
e)\n\n\nAbstract\nDrinfeld’s lemma measures the failure of the Kunneth f
ormula for the etale fundamental group in positive characteristic $p > 0$
in terms of equivariance data under partial Frobenii. In the talk\, I expl
ain a sheaf-theoretic formulation for derived categories of lisse and cons
tructible Weil sheaves on schemes. This is joint work in progress with Tam
ir Hemo and Jakob Scholbach.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Tamiozzo (Imperial)
DTSTART:20210429T150000Z
DTEND:20210429T162000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/44
DESCRIPTION:Title: On torsion in the cohomology of Hilbert modular varieties\nby
Matteo Tamiozzo (Imperial) as part of Recent Advances in Modern p-Adic Geo
metry (RAMpAGe)\n\n\nAbstract\nWe discuss ongoing joint work with Ana Cara
iani concerning vanishing results for the generic part of the cohomology o
f Hilbert modular varieties. A key ingredient is a comparison of the fibre
s of the Hodge-Tate period maps attached to different quaternionic Shimura
varieties\, inspired by the description of their Goren-Oort stratificatio
n given by Tian-Xiao.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamir Hemo (Caltech)
DTSTART:20210527T160000Z
DTEND:20210527T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/45
DESCRIPTION:Title: Unipotent categorical local Langlands correspondence\nby Tamir
Hemo (Caltech) as part of Recent Advances in Modern p-Adic Geometry (RAMp
AGe)\n\n\nAbstract\nWe formulate a categorical form of the local Langlands
conjecture\nthrough perfect algebraic geometry on a certain infinite dime
nsional\nstack classifying F-iscocrystals with additional structure\, anal
ogous to\na conjecture made by Fargues-Scholze. Using the categorical trac
e\nconstruction we obtain the “unipotent part” of the conjecture from\
nBezrukavnikov’s equivalence of two realizations of the affine Hecke\nca
tegory. Joint work in progress with Xinwen Zhu.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Morra (Paris 13)
DTSTART:20210610T160000Z
DTEND:20210610T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/46
DESCRIPTION:Title: Moduli of Fontaine–Laffaille modules and local–global compatib
ility mod p\nby Stefano Morra (Paris 13) as part of Recent Advances in
Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nThe mod $p$-local Langlan
ds program generated from the observation that certain invariants\non loca
l Galois deformation rings can be predicted by the mod $p$ representation
theory of $p$-adic $\\mathbf{GL}_n$. A first attempt to give evidence for
this program is in the expected local–global compatibility\, namely that
the correspondence will be realized in Hecke eigenspaces of the cohomolog
y of locally symmetric spaces with infinite level at p. In this talk we pr
ove one direction of this expectation\, namely that the smooth $\\mathbf{G
L}_n(\\mathbb{Q}_{p^f})$ action on Hecke eigenspaces\nin the mod $p$ cohom
ology of compact unitary groups with infinite level at $p$ determines the\
nlocal Galois parameter at $p$-adic places\, when the latter parameters ar
e Fontaine–Laffaille.\nThis is joint work in progress with D. Le\, B. Le
Hung\, C. Park and Z. Qian.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Mantovan (Caltech)
DTSTART:20210603T160000Z
DTEND:20210603T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/47
DESCRIPTION:Title: Infinitely many primes of basic reduction\nby Elena Mantovan (
Caltech) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\
n\nAbstract\nIn 1987\, Elkies proved that an elliptic curve defined over t
he field of\nrational numbers has infinitely many primes of supersingular
reduction.\nI will discuss a generalization of this result to the case of
special\ncyclic covers of the projective line ramified at 4 points.\nThis
talk is based on joint work in progress with Wanlin Li\, Rachel\nPries an
d Yunqing Tang.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Youcis (IMPAN)
DTSTART:20210513T160000Z
DTEND:20210513T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/48
DESCRIPTION:Title: Geometric coverings of rigid spaces\nby Alex Youcis (IMPAN) as
part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract
\nFrom Tate's uniformization of elliptic curves onwards\, the notion of 'c
overing space'\, and consequently the notion of fundamental groups\, has p
layed a guiding role in the development of rigid geometry. A huge leap for
ward in our understanding of what exactly covering space/fundamental group
might mean in this context was carried out by de Jong in the mid 90s wher
e he was able to form a fundamental group that encompassed both the topolo
gical coverings (e.g. those appear in Tate's uniformization) and finite et
ale coverings. In our current work we propose an extension of those coveri
ng spaces considered by de Jong\, which not only provides a more conceptua
l framework for talking about covering spaces as a whole\, but also is clo
sed under many of the natural geometric operations that de Jong's covering
spaces are not (e.g. disjoint unions and etale localization). Along the w
ay we address some questions posed in de Jong's article\, as well as givin
g a concrete description of the locally constant sheaves in the pro-etale
topology which appears in Scholze's work on p-adic Hodge theory.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Schraen (Paris-Saclay)
DTSTART:20210624T160000Z
DTEND:20210624T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/49
DESCRIPTION:Title: Finite length for cohomological mod p representations of GL2 of a
p-adic field\nby Benjamin Schraen (Paris-Saclay) as part of Recent Adv
ances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nIn the search for
a mod p local Langlands correspondence\, it\nis natural to study the repr
esentations of GL2 of a p-adic field F in\nthe mod p cohomology of Shimura
curves. It is expected that the action\nof GL2(F) on a Galois-isotypic su
bspace of the mod p cohomology of a\ntower of Shimura curves (of fixed tam
e level) has finite length and is\nrelated to the local Galois representat
ion at p. In the case of modular\ncurves\, this is known by the local-glob
al compatibility theorem of\nEmerton. I'll explain how to prove some new c
ases of the finiteness of\nthe length when F is an unramified extension of
Qp. This finiteness is\nrelated to the computation of the Gelfand-Kirillo
v dimension of these\nrepresentations. This is a joint work with Christoph
e Breuil\, Florian\nHerzig\, Yongquan Hu and Stefano Morra.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART:20211005T160000Z
DTEND:20211005T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/50
DESCRIPTION:Title: Bun_G minicourse: Introduction\nby Jared Weinstein (Boston Un
iversity) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n
\n\nAbstract\nThis talk is the first part of a six-part series "$\\mathrm{
Bun}_G$\, Shtukas\, and the Local Langlands Program"\, held Tuesdays and T
hursdays between 5 and 21 October\, 2021.\n\nRecordings and slides will ap
pear here: https://sites.google.com/view/rampageseminar/home\n\nSeries ab
stract: The recent manuscript of Fargues-Scholze aims to "geometrize" the
Langlands program for a p-adic group $G$\, by relating the players in tha
t story to the stack $\\mathrm{Bun}_G$. Following a strategy of V. Laffor
gue\, the main result of [FS] is the construction of an L-parameter attach
ed to a smooth irreducible representation of $G$.\n\nThe goal of this seri
es is to review the main ideas of this work\, and to discuss two related r
esults: progress on the Kottwitz conjecture for local shtuka spaces by Ha
nsen-Kaletha-Weinstein\, and the construction of eigensheaves on $\\mathr
m{Bun}_G$ when $G=\\mathrm{GL}_n$ by Anschütz-le Bras. \n\nTalk abstract:
We will give a historically motivated introduction to the story\, review
ing moduli spaces of $p$-divisible groups\, the Fargues-Fontaine curve\, a
nd the stack $\\mathrm{Bun}_G$ of $G$-bundles on it. We will then define
the moduli spaces of local shtukas\, and state our result on their cohomol
ogy.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasho Kaletha (University of Michigan)
DTSTART:20211007T160000Z
DTEND:20211007T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/51
DESCRIPTION:Title: Bun_G minicourse: Local Langlands\nby Tasho Kaletha (Universi
ty of Michigan) as part of Recent Advances in Modern p-Adic Geometry (RAMp
AGe)\n\n\nAbstract\nThis talk is the second part of a six-part series "$\\
mathrm{Bun}_G$\, Shtukas\, and the Local Langlands Program"\, held Tuesday
s and Thursdays between 5 and 21 October\, 2021.\n\nRecordings and slides
will appear here: https://sites.google.com/view/rampageseminar/home\n\nSe
ries abstract: The recent manuscript of Fargues-Scholze aims to "geometri
ze" the Langlands program for a p-adic group $G$\, by relating the players
in that story to the stack $\\mathrm{Bun}_G$. Following a strategy of V.
Lafforgue\, the main result of [FS] is the construction of an L-parameter
attached to a smooth irreducible representation of $G$.\n\nThe goal of th
is series is to review the main ideas of this work\, and to discuss two re
lated results: progress on the Kottwitz conjecture for local shtuka space
s by Hansen-Kaletha-Weinstein\, and the construction of eigensheaves on $
\\mathrm{Bun}_G$ when $G=\\mathrm{GL}_n$. \n\nTalk abstract: We will revie
w some representation-theoretic inputs to HKW. We’ll begin with reviewin
g the statements of the basic and refined local Langlands correspondence a
nd the status of their proofs. We will then define the relative position o
f two members of a compound L-packet\, which is an input to the Kottwitz c
onjecture\, and the relative position of two regular semi-simple elements
in inner forms. Based on the latter\, we will define a Hecke transfer oper
ator that transfers conjugation-invariant functions between inner forms\,
and discuss its effect on characters of supercuspidal representations.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (Boston University)
DTSTART:20211012T160000Z
DTEND:20211012T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/52
DESCRIPTION:Title: Bun_G minicourse: Lefschetz formula for diamonds\nby Jared We
instein (Boston University) as part of Recent Advances in Modern p-Adic Ge
ometry (RAMpAGe)\n\n\nAbstract\nThis talk is the third part of a six-part
series "$\\mathrm{Bun}_G$\, Shtukas\, and the Local Langlands Program"\, h
eld Tuesdays and Thursdays between 5 and 21 October\, 2021.\n\nSeries abst
ract: The recent manuscript of Fargues-Scholze aims to "geometrize" the L
anglands program for a p-adic group $G$\, by relating the players in that
story to the stack $\\mathrm{Bun}_G$. Following a strategy of V. Lafforgu
e\, the main result of [FS] is the construction of an L-parameter attached
to a smooth irreducible representation of $G$.\n\nThe goal of this series
is to review the main ideas of this work\, and to discuss two related res
ults: progress on the Kottwitz conjecture for local shtuka spaces by Hans
en-Kaletha-Weinstein\, and the construction of eigensheaves on $\\mathrm{
Bun}_G$ when $G=\\mathrm{GL}_n$ by Anschütz-le Bras. \n\nTalk abstract:
In this talk we will discuss a very general form of the Lefschetz-Verdier
trace formula which applies to stacks (both of schemes and of diamonds).
As an application\, we will show that if a locally pro-$p$ group $G$ acts
on a proper diamond $X$\, and if $A$ is a $G$-equivariant $\\ell$-adic she
af on $X$ which is "dualizable" (= universally locally acyclic)\, then the
cohomology $R\\Gamma(X\,A)$ is an admissible representation of $G$\, whos
e Harish-Chandra distribution can be computed in terms of local terms livi
ng on the fixed-point locus of $G$ on $X$.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Hansen (Max Planck Institute for Mathematics)
DTSTART:20211014T160000Z
DTEND:20211014T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/53
DESCRIPTION:Title: Bun_G minicourse: The Kottwitz conjecture\nby David Hansen (M
ax Planck Institute for Mathematics) as part of Recent Advances in Modern
p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nThis talk is the fourth part of a
six-part series "$\\mathrm{Bun}_G$\, Shtukas\, and the Local Langlands Pr
ogram"\, held Tuesdays and Thursdays between 5 and 21 October\, 2021.\n\nR
ecordings and slides will appear here: https://sites.google.com/view/ramp
ageseminar/home\n\nSeries abstract: The recent manuscript of Fargues-Scho
lze aims to "geometrize" the Langlands program for a p-adic group $G$\, by
relating the players in that story to the stack $\\mathrm{Bun}_G$. Follo
wing a strategy of V. Lafforgue\, the main result of [FS] is the construct
ion of an L-parameter attached to a smooth irreducible representation of $
G$.\n\nThe goal of this series is to review the main ideas of this work\,
and to discuss two related results: progress on the Kottwitz conjecture f
or local shtuka spaces by Hansen-Kaletha-Weinstein\, and the construction
of eigensheaves on $\\mathrm{Bun}_G$ when $G=\\mathrm{GL}_n$ by Anschütz
-le Bras. \n\nTalk abstract: In this lecture\, we will give a detailed ske
tch of the proof of the main theorem of [HKW]\, building on the material i
n the first three lectures. The idea that the Kottwitz conjecture should
follow from some form of the Lefschetz trace formula goes back to Harris i
n the '90s. We will try to emphasize the new ingredients which allow us to
implement this idea in full generality.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Anschütz (University of Bonn)
DTSTART:20211019T160000Z
DTEND:20211019T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/54
DESCRIPTION:Title: Bun_G minicourse: The spectral action\nby Johannes Anschütz
(University of Bonn) as part of Recent Advances in Modern p-Adic Geometry
(RAMpAGe)\n\n\nAbstract\nThis talk is the fifth part of a six-part series
"$\\mathrm{Bun}_G$\, Shtukas\, and the Local Langlands Program"\, held Tue
sdays and Thursdays between 5 and 21 October\, 2021.\n\nRecordings and sli
des will appear here: https://sites.google.com/view/rampageseminar/home\n
\nSeries abstract: The recent manuscript of Fargues-Scholze aims to "geom
etrize" the Langlands program for a p-adic group $G$\, by relating the pla
yers in that story to the stack $\\mathrm{Bun}_G$. Following a strategy o
f V. Lafforgue\, the main result of [FS] is the construction of an L-param
eter attached to a smooth irreducible representation of $G$.\n\nThe goal o
f this series is to review the main ideas of this work\, and to discuss tw
o related results: progress on the Kottwitz conjecture for local shtuka s
paces by Hansen-Kaletha-Weinstein\, and the construction of eigensheaves
on $\\mathrm{Bun}_G$ when $G=\\mathrm{GL}_n$ by Anschütz-le Bras. \n\nTal
k abstract: In these last two talks\, the Galois group finally enters the
picture. Let $E$ be a local field and a reductive group $G$ over $E$. Foll
owing Dat-Helm-Kurinczuk-Moss\, Zhu and Fargues-Scholze\, we will first ex
plain how to construct the \\textit{stack of $L$-parameters}\, which is an
ind-Artin-stack parametrizing $\\hat{G}$-valued continuous representation
s of the Weil group of $E$ (for simplicity\, we will restrict our attentio
n to characteristic zero coefficients). Then we will explain how to constr
uct an action (called the \\textit{spectral action}) of the category of pe
rfect complexes on the stack of $L$-parameters on the derived category of
$\\ell$-adic sheaves on $\\mathrm{Bun}_G$. This is the main result of Farg
ues-Scholze and is obtained by combining the general version of the geomet
ric Satake equivalence with a presentation of this category of perfect com
plexes by generators and relations.\nThe existence of the spectral action
allows one to go from the « automorphic side » to the « Galois side »\
, and conversely. In one direction\, we will see that it implies quite dir
ectly the construction of $L$-parameters attached to smooth irreducible re
presentations of $G(E)$. In the other direction\, Fargues formulated in 20
14 a striking conjecture predicting that one can attach to a discrete $L$-
parameter an \\textit{Hecke eigensheaf} on $\\mathrm{Bun}_G$ with nice pro
perties. We will recall what this conjecture says when $G=GL_n$\, and expl
ain how to prove it when the parameter is assumed to be irreducible\, by u
sing the spectral action together with the results of the previous talks.\
n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur-César Le Bras (University of Paris 13)
DTSTART:20211021T160000Z
DTEND:20211021T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/55
DESCRIPTION:Title: Bun_G minicourse: Construction of the eigensheaf\nby Arthur-C
ésar Le Bras (University of Paris 13) as part of Recent Advances in Moder
n p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nThis talk is the sixth part of
a six-part series "$\\mathrm{Bun}_G$\, Shtukas\, and the Local Langlands P
rogram"\, held Tuesdays and Thursdays between 5 and 21 October\, 2021.\n\n
Recordings and slides will appear here: https://sites.google.com/view/ram
pageseminar/home\n\nSeries abstract: The recent manuscript of Fargues-Sch
olze aims to "geometrize" the Langlands program for a p-adic group $G$\, b
y relating the players in that story to the stack $\\mathrm{Bun}_G$. Foll
owing a strategy of V. Lafforgue\, the main result of [FS] is the construc
tion of an L-parameter attached to a smooth irreducible representation of
$G$.\n\nThe goal of this series is to review the main ideas of this work\,
and to discuss two related results: progress on the Kottwitz conjecture
for local shtuka spaces by Hansen-Kaletha-Weinstein\, and the constructio
n of eigensheaves on $\\mathrm{Bun}_G$ when $G=\\mathrm{GL}_n$ by Anschüt
z-le Bras. \n\nTalk abstract: In these last two talks\, the Galois group f
inally enters the picture. Let $E$ be a local field and a reductive group
$G$ over $E$. Following Dat-Helm-Kurinczuk-Moss\, Zhu and Fargues-Scholze\
, we will first explain how to construct the \\textit{stack of $L$-paramet
ers}\, which is an ind-Artin-stack parametrizing $\\hat{G}$-valued continu
ous representations of the Weil group of $E$ (for simplicity\, we will res
trict our attention to characteristic zero coefficients). Then we will exp
lain how to construct an action (called the \\textit{spectral action}) of
the category of perfect complexes on the stack of $L$-parameters on the de
rived category of $\\ell$-adic sheaves on $\\mathrm{Bun}_G$. This is the m
ain result of Fargues-Scholze and is obtained by combining the general ver
sion of the geometric Satake equivalence with a presentation of this categ
ory of perfect complexes by generators and relations.\nThe existence of th
e spectral action allows one to go from the « automorphic side » to the
« Galois side »\, and conversely. In one direction\, we will see that it
implies quite directly the construction of $L$-parameters attached to smo
oth irreducible representations of $G(E)$. In the other direction\, Fargue
s formulated in 2014 a striking conjecture predicting that one can attach
to a discrete $L$-parameter an \\textit{Hecke eigensheaf} on $\\mathrm{Bun
}_G$ with nice properties. We will recall what this conjecture says when $
G=GL_n$\, and explain how to prove it when the parameter is assumed to be
irreducible\, by using the spectral action together with the results of th
e previous talks.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akhil Mathew (University of Chicago)
DTSTART:20211104T160000Z
DTEND:20211104T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/56
DESCRIPTION:Title: On the $\\mathbb{Z}_p(i)$ of Bhatt-Morrow-Scholze\nby Akhil Ma
thew (University of Chicago) as part of Recent Advances in Modern p-Adic G
eometry (RAMpAGe)\n\n\nAbstract\nI will explain a description of the $\\ma
thbb{Z}_p(i)$ complexes defined\nby Bhatt-Morrow-Scholze\, as an integral
refinement of\nFontaine-Messing syntomic cohomology\, on a class of $p$-ad
ic formal\nschemes (including regular noetherian ones and formally smooth
schemes\nover perfectoids) satisfying the "Segal conjecture". This extends
a\nnumber of comparison results in the literature. Joint with Bhargav\nBh
att.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Kisin (Harvard University)
DTSTART:20211111T180000Z
DTEND:20211111T192000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/58
DESCRIPTION:Title: Essential dimension via prismatic cohomology\nby Mark Kisin (H
arvard University) as part of Recent Advances in Modern p-Adic Geometry (R
AMpAGe)\n\n\nAbstract\nLet $f\\colon Y→X$ be a finite covering map of co
mplex algebraic varieties. The essential dimension of f is the smallest in
teger e such that\, birationally\, $f$ arises as the pullback of a coverin
g $Y′→X′$ of dimension $e$\, via a map $X→X′$. This invariant go
es back to classical questions about reducing the number of parameters in
a solution to a general nth degree polynomial\, and appeared in work of Kr
onecker and Klein on solutions of the quintic. \n\nI will report on joint
work with Benson Farb and Jesse Wolfson\, where we introduce a new techniq
ue\, using prismatic cohomology\, to obtain lower bounds on the essential
dimension of certain coverings. For example\, we show that for an abelian
variety $A$ of dimension $g$ the multiplication by $p$ map $A→A$ has ess
ential dimension $g$ for almost all primes $p$.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Boxer & Vincent Pilloni (Orsay)
DTSTART:20211202T170000Z
DTEND:20211202T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/59
DESCRIPTION:Title: Higher Coleman Theory I\nby George Boxer & Vincent Pilloni (Or
say) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nA
bstract\nWe have developed local cohomology techniques to study the cohere
nt cohomology of Shimura varieties. The local cohomology groups which appe
ar are a generalization of overconvergent modular forms studied by Coleman
and many others. \n\nTentative plan of the lectures : \n1) Overview of th
e results and analogy with classical representation theory \n2) Definition
of the local cohomology\, vanishing theorems and slope estimates. \n3) Ei
genvarieties and applications.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Boxer & Vincent Pilloni (Orsay)
DTSTART:20211209T170000Z
DTEND:20211209T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/60
DESCRIPTION:Title: Higher Coleman Theory II\nby George Boxer & Vincent Pilloni (O
rsay) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\n
Abstract\nWe have developed local cohomology techniques to study the coher
ent cohomology of Shimura varieties. The local cohomology groups which app
ear are a generalization of overconvergent modular forms studied by Colema
n and many others. \n\nTentative plan of the lectures : \n1) Overview of t
he results and analogy with classical representation theory \n2) Definitio
n of the local cohomology\, vanishing theorems and slope estimates. \n3) E
igenvarieties and applications.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Boxer & Vincent Pilloni (Orsay)
DTSTART:20211216T170000Z
DTEND:20211216T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/61
DESCRIPTION:Title: Higher Coleman Theory III\nby George Boxer & Vincent Pilloni (
Orsay) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\
nAbstract\nWe have developed local cohomology techniques to study the cohe
rent cohomology of Shimura varieties. The local cohomology groups which ap
pear are a generalization of overconvergent modular forms studied by Colem
an and many others. \n\nTentative plan of the lectures : \n1) Overview of
the results and analogy with classical representation theory \n2) Definiti
on of the local cohomology\, vanishing theorems and slope estimates. \n3)
Eigenvarieties and applications.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Anschütz (Bonn)
DTSTART:20220202T170000Z
DTEND:20220202T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/62
DESCRIPTION:Title: On the p-adic theory of local models I\nby Johannes Anschütz
(Bonn) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\
nAbstract\nThe first talk concerns the \\'etale cohomology of the v-sheaf
local models. After motivating the definition of v-sheaf local models we w
ill determine their special fibers by calculating the nearby cycles of Sat
ake sheaves.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Lourenço (Bonn)
DTSTART:20220209T170000Z
DTEND:20220209T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/63
DESCRIPTION:Title: On the p-adic theory of local models II\nby João Lourenço (B
onn) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nA
bstract\nThis second talk (based on joint work with Anschütz–Gleason–
Richarz) concerns the Scholze–Weinstein conjecture on the representabili
ty of v-sheaf local models for geometric conjugacy classes of minuscule co
weights. I'll start by reviewing previously known instances of local model
s in PEL cases by Rapoport–Zink\, and also via power series Grassmannian
s by Pappas–Zhu. I'll briefly explain how to slightly refine the latter
(joint with Fakhruddin–Haines–Richarz). Building on this\, I'll explai
n the comparison of p-adic admissible loci in the Witt Grassmannian with t
hose found in power series Grassmannians. Next\, I'll prove the\nspecializ
ation principle for sufficiently nice kimberlites\, which include v-sheaf
local models (even for non-minuscule cocharacters). Finally\, I'm going to
explain how to compute the specialization mapping in families\, deducing
the Scholze–Weinstein conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lue Pan (Princeton)
DTSTART:20220119T170000Z
DTEND:20220119T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/64
DESCRIPTION:Title: On the p-adic Hodge structure of completed cohomology of modular c
urves I\nby Lue Pan (Princeton) as part of Recent Advances in Modern p
-Adic Geometry (RAMpAGe)\n\n\nAbstract\nLet $p$ be a prime. I plan to expl
ain how to read the $p$-adic Hodge structure of the $p$-adically completed
cohomology of modular curves by studying the $p$-adic geometry of the mod
ular curves at infinite level. One main tool is the relative Sen theory (a
lso called $p$-adic Simpson correspondence) which provides a first-order d
ifferential equation and allows us to apply differential operators pulled
back from the flag variety along the Hodge-Tate period map.\n\nLecture (1)
: Hodge-Tate structure\nLecture (2): de Rham structure\n\nIf time permits\
, I will also discuss several applications.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lue Pan (Princeton)
DTSTART:20220126T170000Z
DTEND:20220126T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/65
DESCRIPTION:Title: On the p-adic Hodge structure of completed cohomology of modular c
urves II\nby Lue Pan (Princeton) as part of Recent Advances in Modern
p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nLet $p$ be a prime. I plan to exp
lain how to read the $p$-adic Hodge structure of the $p$-adically complete
d cohomology of modular curves by studying the $p$-adic geometry of the mo
dular curves at infinite level. One main tool is the relative Sen theory (
also called $p$-adic Simpson correspondence) which provides a first-order
differential equation and allows us to apply differential operators pulled
back from the flag variety along the Hodge-Tate period map.\n\nLecture (1
): Hodge-Tate structure\nLecture (2): de Rham structure\n\nIf time permits
\, I will also discuss several applications.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jackson Morrow (Berkeley)
DTSTART:20220302T170000Z
DTEND:20220302T182000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/66
DESCRIPTION:Title: On p-adic uniformization of abelian varieties with good reduction<
/a>\nby Jackson Morrow (Berkeley) as part of Recent Advances in Modern p-A
dic Geometry (RAMpAGe)\n\n\nAbstract\nInvestigating the p-adic integration
map constructed by J.-M. Fontaine during the 90's\, which is the main too
l for proving the Hodge--Tate decomposition of the Tate module of an abeli
an variety over a p-adic field\, we realized that the group of p-adic poin
ts of the above-named abelian variety\, satisfying certain hypothesis\, ha
s a type of p-adic uniformization which was not remarked before. This is j
oint work with A. Iovita and A. Zaharescu.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siyan Daniel Li-Huerta (Harvard)
DTSTART:20220323T160000Z
DTEND:20220323T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/67
DESCRIPTION:Title: The plectic conjecture over local fields\nby Siyan Daniel Li-H
uerta (Harvard) as part of Recent Advances in Modern p-Adic Geometry (RAMp
AGe)\n\n\nAbstract\nThe étale cohomology of varieties over $\\mathbf{Q}$
enjoys a Galois action. In the case of Hilbert modular varieties\, Neková
ř-Scholl observed that this Galois action on the level of cohomology exte
nds to a much larger profinite group: the plectic group. They conjectured
that this extension holds even on the level of complexes\, as well as for
more general Shimura varieties.\n\nWe present a proof of the analogue of t
his conjecture for local Shimura varieties. This implies that\, for p-adic
ally uniformized global Shimura varieties\, we obtain an action of the loc
al plectic group on the level of complexes. The proof crucially uses Fargu
es–Scholze's results on the cohomology of moduli spaces of local shtukas
.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Johansson (Chalmers/Gothenburg)
DTSTART:20220504T160000Z
DTEND:20220504T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/68
DESCRIPTION:Title: Signs of a p-adic geometric Langlands correspondence: part I\n
by Christian Johansson (Chalmers/Gothenburg) as part of Recent Advances in
Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nRecent developments in th
e geometrization of local Langlands correspondence suggests\, among other
things\, that the category of smooth complex representations of a p-adic g
roup can be embedded fully faithfully into a category of ind-coherent shea
ves on a moduli space of Weil-Deligne representations. For the p-adic loca
l Langlands correspondence\, a geometric perspective is more speculative.
In these talks we will outline the construction of a fully faithful contra
variant embedding of the category of p-adic locally admissible representat
ions of GL(2\,Qp) into a suitable category of coherent sheaves on the modu
li stack of 2-dimensional p-adic representations of Gal(Qp-bar/Qp)\, const
ructed by Wang-Erickson. We will also discuss analogous statements for SL(
2\,Qp)\, highlighting the role of endoscopy.\n\n\nThis is joint work betwe
en Christian Johansson\, James Newton and Carl Wang-Erickson.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shizhang Li (University of Michigan)
DTSTART:20220518T160000Z
DTEND:20220518T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/70
DESCRIPTION:Title: u-torsions in Breuil-Kisin prismatic cohomology\nby Shizhang L
i (University of Michigan) as part of Recent Advances in Modern p-Adic Geo
metry (RAMpAGe)\n\n\nAbstract\nI shall report a joint work with Tong Liu\,
in which we discuss a tiny piece of the Breuil--Kisin prismatic cohomolog
y module of a general smooth proper scheme X over a p-adic ring of integer
s O_K. I will try to explain why this tiny piece can be interesting from b
oth algebro-gemetric and number-theoretic point of views. Also planned is
a concrete description of an interesting example extracted from the work o
f Bhatt--Morrow--Scholze\, giving rise to an example negating a prediction
that Breuil made some 20 years ago.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Wang-Erickson (University of Pittsburgh)
DTSTART:20220525T160000Z
DTEND:20220525T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/71
DESCRIPTION:Title: Signs of a p-adic geometric Langlands correspondence: part II\
nby Carl Wang-Erickson (University of Pittsburgh) as part of Recent Advanc
es in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nRecent developments
in the geometrization of local Langlands correspondence suggests\, among o
ther things\, that the category of smooth complex representations of a $p$
-adic group can be embedded fully faithfully into a category of ind-cohere
nt sheaves on a moduli space of Weil-Deligne representations. For the $p$-
adic local Langlands correspondence\, a geometric perspective is more spec
ulative. In these talks we will outline the construction of a fully faithf
ul contravariant embedding of the category of $p$-adic locally admissible
representations of $\\mathrm{GL}(2\,\\mathbb{Q}_p)$ into a suitable catego
ry of coherent sheaves on the moduli stack of 2-dimensional $p$-adic repre
sentations of $\\mathrm{Gal}(\\overline{\\mathbb{Q}_p}/\\mathbb{Q}_p)$. In
this second talk in particular\, we will emphasize the explicit and compu
table nature of the moduli stack of Galois representations and certain she
aves on it.\n\nAttendance at the prior talk in this series will not be pre
sumed.\n\nThis is joint work between Christian Johansson\, James Newton an
d Carl Wang-Erickson.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Esteban Rodriguez Camargo (Ecole Normale Supérieure de Lyon)
DTSTART:20220601T160000Z
DTEND:20220601T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/72
DESCRIPTION:Title: Solid locally analytic representations of $p$-adic Lie groups\
nby Juan Esteban Rodriguez Camargo (Ecole Normale Supérieure de Lyon) as
part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\
nMotivated from the works of Lazard\, Schneider-Teitelbaum and Emerton\, a
nd from the theory of condensed mathematics developed by Clausen and Schol
ze\, we give new foundations for the theory of locally analytic representa
tions of (compact) $p$-adic Lie groups. In this talk we will discuss how t
he interpretation of taking analytic vectors à la Emerton shows that the
concept of being an analytic representation for some open compact subgroup
is the same as being a module over some analytic distribution algebra. Th
is observation algebraizes the theory of locally analytic representations\
, and some comparison theorems of Lazard and Tamme on continuous - local
ly analytic - Lie algebra cohomology hold for general solid representatio
ns by basic homological algebra arguments. Joint work with Joaquín Rodrig
ues Jacinto.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bhargav Bhatt (IAS/Princeton)
DTSTART:20220810T160000Z
DTEND:20220810T172000Z
DTSTAMP:20260404T110653Z
UID:RAMpAGe/73
DESCRIPTION:Title: Prismatic F-gauges (final RAMpAGe talk!)\nby Bhargav Bhatt (IA
S/Princeton) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe
)\n\n\nAbstract\nRecording: https://bostonu.zoom.us/rec/share/DzQW6dw2X-T
8RhqlthoGxAO0kD4hYmOKebIh8nFxnRh9U-rz15TrtPG2KgSuz3zZ.YaFrVJvWNFbn6xLV\n\n
Notes: https://drive.google.com/file/d/1PWW_guqKGBvWsrnddjX18XdTKX2KbeLG/v
iew?usp=sharing\n\nPrismatic F-gauges are the natural coefficient systems
for prismatic cohomology\, analogous to variations of Hodge structures in
classical Hodge theory. This talk will describe a couple of equivalent per
spectives on this notion\, and then present evidence suggesting that prism
atic F-gauges over Spf(Z_p) might provide a meaningful notion of crystalli
nity for representations of the absolute Galois group of Q_p with torsion
coefficients. This is joint work in progress with Jacob Lurie\, building o
n work of Drinfeld.\n
LOCATION:https://stable.researchseminars.org/talk/RAMpAGe/73/
END:VEVENT
END:VCALENDAR