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SUMMARY:Christian Liedtke (https://www.groups.ma.tum.de/algebra/liedtke/)
DTSTART:20210202T120000Z
DTEND:20210202T140000Z
DTSTAMP:20260404T095735Z
UID:ShafarevichSeminar/1
DESCRIPTION:Title: Quotient singularities in positive characteristic\nb
y Christian Liedtke (https://www.groups.ma.tum.de/algebra/liedtke/) as par
t of Shafarevich seminar\n\n\nAbstract\nWe study isolated quotient singula
rities by finite group schemes in positive characteristic. We compute inva
riants\, study the uniqueness of the quotient presentation\, and compute s
ome\ndeformation spaces. A special emphasis is laid on the dichotomy betwe
en quotient singularities by linearly reductive group schemes and by group
schemes that are not linearly reductive. We essentially classify the line
arly reductive ones\, give applications\, and make some conjectures. This
is joint work with Gebhard Martin (Bonn) and Yuya Matsumoto (Tokyo).\n
LOCATION:https://stable.researchseminars.org/talk/ShafarevichSeminar/1/
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SUMMARY:Valery Lunts (Indiana University Bloomington)
DTSTART:20210209T120000Z
DTEND:20210209T140000Z
DTSTAMP:20260404T095735Z
UID:ShafarevichSeminar/2
DESCRIPTION:Title: Neron-Severi Lie algebra\, group of autoequivalences of
the derived category\, and monodromy\nby Valery Lunts (Indiana Univers
ity Bloomington) as part of Shafarevich seminar\n\n\nAbstract\nLet $X$ be
a smooth complex projective manifold\, $G^{eq}(X)\\subset GL(H(X))$ --- th
e image of the group $Aut(D(X))$ in the group of automorphisms of $H(X)$.
First I will explain about the\nrelation of the group $G^{eq}(X)$ and the
Neron-Severi Lie algebra. Then I plan to discuss the conjecture of Kontsev
ich on the relation of the group $G^{eq}(X)$ (if $X$ is CY) with the monod
romy group of the mirror symmetric family.\n
LOCATION:https://stable.researchseminars.org/talk/ShafarevichSeminar/2/
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SUMMARY:Yuri Prokhorov (Steklov Mathematical Institute of RAS\, NRU HSE)
DTSTART:20210216T120000Z
DTEND:20210216T140000Z
DTSTAMP:20260404T095735Z
UID:ShafarevichSeminar/3
DESCRIPTION:Title: Tetragonal conic bundles\nby Yuri Prokhorov (Steklov
Mathematical Institute of RAS\, NRU HSE) as part of Shafarevich seminar\n
\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ShafarevichSeminar/3/
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BEGIN:VEVENT
SUMMARY:Ivan Panin (St. Petersburg Department of Steklov Mathematical Inst
itute of RAS)
DTSTART:20210224T120000Z
DTEND:20210224T140000Z
DTSTAMP:20260404T095735Z
UID:ShafarevichSeminar/4
DESCRIPTION:Title: Some results on injectivity and purity in the mixed char
acteristic case\nby Ivan Panin (St. Petersburg Department of Steklov M
athematical Institute of RAS) as part of Shafarevich seminar\n\n\nAbstract
\nLet $\\mathcal O$ be a discrete valuation ring of mixed\ncharacteristic.
For certain class of abelian group presheaves on the\ncategory of $\\math
cal O$-smooth schemes we will discuss injectivity and purity\ntheorems. In
particular\, we will discuss the Grothendieck-Serre\nconjecture for some
classical groups. We will focus on statements\nand methods. Proofs will be
only sketched.\n
LOCATION:https://stable.researchseminars.org/talk/ShafarevichSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Levine (Duisburg-Essen University)
DTSTART:20210302T120000Z
DTEND:20210302T140000Z
DTSTAMP:20260404T095735Z
UID:ShafarevichSeminar/5
DESCRIPTION:Title: Some quadratic conductor formulas\nby Marc Levine (D
uisburg-Essen University) as part of Shafarevich seminar\n\n\nAbstract\nA
smooth projective variety over a\nfield k defines a dualizable object in t
he motivic stable homotopy\nover k\, and thereby an Euler characteristic i
n the endomorphism ring\nof the unit. A theorem of Morel identifies this e
ndomorphism ring\nwith the Grothendieck-Witt ring of quadratic forms over
k and with\nA. Raksit\, we have shown that this quadratic Euler characteri
stic is\ngiven by the intersection form on Hodge cohomology. We use the\nc
omputation of Hodge cohomology of hypersurfaces via the Jacobian\nring to
give an explicit description of the categorical Euler\ncharacteristic of a
smooth hypersurface and use this to give\nexamples of a quadratic conduct
or formula for certain\ndegenerations. There are mysterious "error terms"
that makes the\nformula deviate from what one might expect at first glance
. These\nerror terms disappear over the complex numbers and also over the\
nreal numbers\, but are in general non-zero.\n
LOCATION:https://stable.researchseminars.org/talk/ShafarevichSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Peternell (Bayreuth University)
DTSTART:20210309T120000Z
DTEND:20210309T140000Z
DTSTAMP:20260404T095735Z
UID:ShafarevichSeminar/6
DESCRIPTION:Title: Projective flatness and applications to uniformization\nby Thomas Peternell (Bayreuth University) as part of Shafarevich semin
ar\n\n\nAbstract\nI will discuss a Chern class criterion to when a semista
ble sheaf on a mildly singular variety is projectively flat and apply this
to the uniformization of varieties with nef anticanonical bundles ("singu
lar semipositive Ricci").\n
LOCATION:https://stable.researchseminars.org/talk/ShafarevichSeminar/6/
END:VEVENT
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SUMMARY:Alexander Efimov (Steklov Mathematical Institute of RAS)
DTSTART:20210316T120000Z
DTEND:20210316T140000Z
DTSTAMP:20260404T095735Z
UID:ShafarevichSeminar/7
DESCRIPTION:Title: Nuclear modules over proper DG algebras\nby Alexande
r Efimov (Steklov Mathematical Institute of RAS) as part of Shafarevich se
minar\n\n\nAbstract\nI will explain a certain construction of a dualizable
presentable DG category Nuc(A) of "nuclear modules" over a proper DG alge
bra A. As a special case this construction gives the category of nuclear m
odules on an affine formal scheme (more precisely\, its "unbounded" versio
n)\, which was defined recently by Clausen and Scholze. For a smooth and p
roper DG algebra A the category Nuc(A) is equivalent to the usual category
of A-modules.\n\nI will also explain that this construction is a special
case of internal Hom in an appropriate symmetric monoidal category (where
the objects are dualizable presentable DG categories\, and the morphisms a
re strongly continuous functors).\n
LOCATION:https://stable.researchseminars.org/talk/ShafarevichSeminar/7/
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SUMMARY:Umberto Zannier (Scuola Normale Superiore\, Pisa)
DTSTART:20210323T120000Z
DTEND:20210323T140000Z
DTSTAMP:20260404T095735Z
UID:ShafarevichSeminar/8
DESCRIPTION:Title: Abelian varieties not isogenous to any Jacobian\nby
Umberto Zannier (Scuola Normale Superiore\, Pisa) as part of Shafarevich s
eminar\n\n\nAbstract\nIt is well known that in dimension $g\\ge 4$ there e
xist complex abelian varieties not isogenous to any Jacobian. A question o
f Katz and Oort asked whether one can find\nsuch examples over the field o
f algebraic numbers. This was answered affirmatively by Oort-Chai under th
e André-Oort conjecture\, and by Tsimerman unconditionally. They gave exa
mples within Complex Multiplication. In joint work with Masser\, by means
of a completely\ndifferent method\, we proved that in a sense the general
abelian variety over $\\overline{\\mathbb Q}$ is indeed not isogenous to a
ny Jacobian. I shall illustrate the basic principles of the proofs.\n
LOCATION:https://stable.researchseminars.org/talk/ShafarevichSeminar/8/
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