Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

Equipe(s) : fa, tn,
Responsables :Alexis Bouthier, Benoît Stroh
Email des responsables : alexis.bouthier@imj-prg.fr, benoit.stroh@imj-prg.fr
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Orateur(s) David HELM - Imperial College,
Titre A categorical Deligne-Langlands correspondence for split reductive groups
Date03/05/2021
Horaire10:30 à 12:00
Diffusion
RésumeLet G be a split reductive group over a p-adic field F. We construct a natural coherent sheaf on the moduli stack of unipotent Langlands paramters for G, called the coherent Springer sheaf, whose self-Ext algebra is naturally isomorphic to the Iwahori Hecke algebra for G. As a consequence we deduce the existence of a fully faithful embedding of the Iwahori block of Rep(G) into the derived category of ind-coherent sheaves on the moduli stack of Langlands parameters. For G = GL_n we can go further and construct a fully faithful embedding of the category of all smooth representations of G into this derived category.
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