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SUMMARY:Cycles on splitting models of Shimura varieties [MPIM]
DTSTART:20260506T130500Z
DTEND:20260506T150000Z
DTSTAMP:20260508T062600Z
UID:indico-event-1310@math-events.uni-bonn.de
DESCRIPTION:Speakers: Thibaud van den Hove (MPIM)\n\nOberseminar Arithmeti
 c Geometry and Representation Theory\nI will explain how to construct exot
 ic Hecke correspondences between the special fibers of different PEL type 
 Shimura varieties\, at possibly ramified primes. These can be used to cons
 truct new geometric realizations of the Jacquet-Langlands correspondence\,
  as well as verify generic instances of the Tate conjecture for the specia
 l fibers of these Shimura varieties\, generalizing the work of Xiao-Zhu in
  the unramified case. The key is to resolve the integral models by the spl
 itting models of Pappas-Rapoport.\nIn the first part of the talk\, I will 
 recall the splitting models of Shimura varieties\, and explain how they ca
 n be used to construct exotic Hecke correspondences. By using a part of th
 e categorical local Langlands correspondence\, I will then deduce geometri
 c realizations of the Jacquet-Langlands correspondence.\nIn the second par
 t of the talk\, I will introduce splitting versions of the affine Deligne-
 Lusztig varieties\, and explain how they can be applied to the Tate conjec
 ture for the special fibers of certain Shimura varieties.\n \n \n\nhttps
 ://math-events.uni-bonn.de/event/1310/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1310/
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