# Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

 Equipe(s) : fa, tn, Responsables : Alexis Bouthier, Cong Xue Email des responsables : alexis.bouthier@imj-prg.fr, cong.xue@imj-prg.fr Salle : Adresse : Description

 Orateur(s) Alexander Ivanov - IMJ-PRG, Titre Affine Deligne-Lusztig theory Date 03/10/2016 Horaire 10:30 à 12:00 Diffusion Résume The classical Deligne-Lusztig theory gives a geometric tool to construct representations of the finite group of rational points of a reductive group over a finite field. We develop an affine version of this, by constructing families of extended affine Deligne-Lusztig varieties attached to a reductive group $G$ over a local field. The cohomology of (certain covers of) these varieties conjecturally allows to realize the local Langlands correspondence and the automorphic induction of characters of maximal tori in $G$. We show this conjecture for $G = \mathrmGL_2$ and at most tamely ramified tori (and all characters of arbitrary deep level). Salle Adresse