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SUMMARY:Igusa stacks and the cohomology of Shimura varieties [MPIM]
DTSTART:20241129T130500Z
DTEND:20241129T150000Z
DTSTAMP:20260416T084100Z
UID:indico-event-97@math-events.uni-bonn.de
DESCRIPTION:Speakers: Pol van Hoften (VU Amsterdam)\n\nhttps://www.mpim-bo
 nn.mpg.de/node/13732\nAssociated to a modular form f is a two-dimensional 
 Galois representation whose Frobenius eigenvalues can be expressed in term
 s of the Fourier coefficients of f\, using a formula known as the Eichler-
 -Shimura congruence relation. This relation was proved by Eichler--Shimura
  and Deligne by analyzing the mod p (bad) reduction of the modular curve o
 f level ?0(p). In this talk\, I will discuss joint work with Patrick Danie
 ls\, Dongryul Kim and Mingjia Zhang\, where we give a new proof of this co
 ngruence relation that happens "entirely on the rigid generic fibre". More
  precisely\, we prove a compatibility result between the compactly cohomol
 ogy of Shimura varieties of Hodge type and the Fargues--Scholze semisimple
  local Langlands correspondence\, generalizing the Eichler--Shimura relati
 on of Blasius-Rogawski. Our proof makes crucial use of the Igusa stacks th
 at we construct\, generalizing earlier work of Zhang in the PEL case.\n\nh
 ttps://math-events.uni-bonn.de/event/97/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/97/
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