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SUMMARY:Teppei Takamatsu (Kyoto University)
DTSTART:20250410T060000Z
DTEND:20250410T070000Z
DTSTAMP:20260404T111326Z
UID:CUHKNT/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CUHKN
 T/1/">On quasi-Frobenius-split singularities</a>\nby Teppei Takamatsu (Kyo
 to University) as part of CUHK Number Theory Online Seminar\n\n\nAbstract\
 nIn algebraic geometry of positive characteristic\, singularities defined 
 by the Frobenius map\, including the notion of Frobenius-splitting\, have 
 played a crucial role. \nYobuko recently introduced the notion of quasi-F-
 splitting and F-split heights\, which generalize and quantify the notion o
 f Frobenius-splitting\, and proved that F-split heights coincide with Arti
 n-Mazur heights for Calabi-Yau varieties. This notion is defined for purel
 y positive characteristic varieties\, but the ring of Witt vectors\, which
  is a mixed characteristic object\, makes an essential role in the definit
 ion. \n\nIn this talk\, I present several criteria for quasi-F-splitting a
 nd their applications. This talk is based on joint research with T. Kawaka
 mi\, H. Tanaka\, J. Witaszek\, F. Yobuko\, and S. Yoshikawa.\n
LOCATION:https://stable.researchseminars.org/talk/CUHKNT/1/
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SUMMARY:Qiao He (Columbia University)
DTSTART:20250523T013000Z
DTEND:20250523T023000Z
DTSTAMP:20260404T111326Z
UID:CUHKNT/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CUHKN
 T/2/">Height pairing on Shimura curve revisited and a general conjecture f
 or GSpin Shimura varieties</a>\nby Qiao He (Columbia University) as part o
 f CUHK Number Theory Online Seminar\n\n\nAbstract\nIn their paper "Height 
 pairings on Shimura curves and p-adic uniformization" (Invent\, 2000)\, Ku
 dla and Rapoport studied intersections of special cycles on Shimura curves
  and related it with derivative of Eisenstein series\, which is one of the
  key ingredient to prove arithmetic inner product formula for Shimura curv
 es (a variant/generalization of Gross-Zagier formula). In this talk\, we w
 ill revisit Kudla and Rapoport's formula by incorporating it into a genera
 l conjecture for the GSpin Shimura variety. As evidence of the conjecture\
 , we also discuss the proof for the self product of Shimura curves case. T
 his is a joint work with Baiqing Zhu.\n\nMeeting ID 988 4193 7996\n\nPassw
 ord 097741\n
LOCATION:https://stable.researchseminars.org/talk/CUHKNT/2/
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