Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

Equipe(s) : fa, tn,
Responsables :Alexis Bouthier, Francesco Lemma
Email des responsables : alexis.bouthier@imj-prg.fr, francesco.lemma(at)imj-prg.fr
Salle :
Adresse :
Description

Orateur(s) Pol van Hoften - VU Amsterdam,
Titre Igusa stacks and the cohomology of Shimura varieties
Date10/06/2024
Horaire10:30 à 12:00
Diffusion
Résume

Associated to a modular form f is a two-dimensional Galois representation whose Frobenius eigenvalues can be expressed in terms 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 of level Γ0(p). In this talk, I will discuss joint work with Patrick Daniels, Dongryul Kim and Mingjia Zhang, where we give a new proof of this congruence relation that happens "entirely on the generic fibre". More precisely, we prove a compatibility result between the compactly supported cohomology of Shimura varieties of Hodge type and the Fargues—Scholze semisimple local Langlands correspondence, using Igusa stacks that we construct.

Salle1016
AdresseSophie Germain
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