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 :

Orateur(s) Konrad Zou - Bonn,
Titre Categorical local Langlands for GL_n: the irreducible case with integral coefficients
Horaire10:30 à 12:00

Fargues and Scholze conjecture a Hecke-equivariant equivalence of categories between certain coherent sheaves on the stack of Langlands parameters and compact objects in the category of lisse-etale sheaves on Bun_G. We will discuss how to prove this conjecture for irreducible parameters for GL_n, with integral coefficients. It turns out that this needs surprisingly little knowledge about the spaces involved, the non-formal input is the cardinality of the Fargues-Scholze L-packets and genericity of their members. The formal input is about localizations of categories over schemes, which we will discuss. If time permits we will also discuss the t-exactness of this equivalence.

AdresseSophie Germain