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SUMMARY:Teppei Takamatsu (Kyoto University)
DTSTART:20250410T060000Z
DTEND:20250410T070000Z
DTSTAMP:20260422T225847Z
UID:CUHKNT/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CUHKNT/1/">O
 n quasi-Frobenius-split singularities</a>\nby Teppei Takamatsu (Kyoto Univ
 ersity) as part of CUHK Number Theory Online Seminar\n\n\nAbstract\nIn alg
 ebraic 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-splitti
 ng and F-split heights\, which generalize and quantify the notion of Frobe
 nius-splitting\, and proved that F-split heights coincide with Artin-Mazur
  heights for Calabi-Yau varieties. This notion is defined for purely posit
 ive characteristic varieties\, but the ring of Witt vectors\, which is a m
 ixed characteristic object\, makes an essential role in the definition. \n
 \nIn this talk\, I present several criteria for quasi-F-splitting and thei
 r applications. This talk is based on joint research with T. Kawakami\, H.
  Tanaka\, J. Witaszek\, F. Yobuko\, and S. Yoshikawa.\n
LOCATION:https://researchseminars.org/talk/CUHKNT/1/
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SUMMARY:Qiao He (Columbia University)
DTSTART:20250523T013000Z
DTEND:20250523T023000Z
DTSTAMP:20260422T225847Z
UID:CUHKNT/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CUHKNT/2/">H
 eight pairing on Shimura curve revisited and a general conjecture for GSpi
 n Shimura varieties</a>\nby Qiao He (Columbia University) as part of CUHK 
 Number Theory Online Seminar\n\n\nAbstract\nIn their paper "Height pairing
 s on Shimura curves and p-adic uniformization" (Invent\, 2000)\, Kudla and
  Rapoport studied intersections of special cycles on Shimura curves and re
 lated it with derivative of Eisenstein series\, which is one of the key in
 gredient to prove arithmetic inner product formula for Shimura curves (a v
 ariant/generalization of Gross-Zagier formula). In this talk\, we will rev
 isit Kudla and Rapoport's formula by incorporating it into a general conje
 cture for the GSpin Shimura variety. As evidence of the conjecture\, we al
 so discuss the proof for the self product of Shimura curves case. This is 
 a joint work with Baiqing Zhu.\n\nMeeting ID 988 4193 7996\n\nPassword 097
 741\n
LOCATION:https://researchseminars.org/talk/CUHKNT/2/
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