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 :

Orateur(s) Maarten SOLLEVELD - Radboud Universiteit Nijmegen,
Titre Graded Hecke algebras and equivariant sheaves in the local Langlands program
Horaire10:30 à 12:00
RésumeIt has been conjectured that the local Langlands correspondence for a reductive p-adic group G (itself also partly conjectural) can be categorified. Then it should relate the category of complex smooth G-representations with a category of equivariant sheaves on a variety of Langlands parameters for G. If it exists, such a categorification will probably arise via Hecke algebras. In this talk we will discuss several steps in this direction. Our main players will be graded Hecke algebras, which appear both on the p-adic side on the Galois side of the local Langlands program. We will see that graded Hecke algebras can not only be constructed in terms of generators and relations, but also geometrically, as endomorphism algebras of certain equivariant constructible sheaves. That leads to comparison theorems between derived categories of modules of graded Hecke algebras and derived categories of equivariant sheaves. We can apply that in the local Langlands program, conjecturally for all reductive p-adic groups and certainly for some well-known groups. From that we obtain a comparison between the derived category of finite length smooth G-representation and derived categories of equivariant constructible sheaves on complex varieties related to L-parameters.
AdresseSophie Germain