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
Salle :
Adresse :

Orateur(s) Sam Raskin - UT Austin,
Titre Geometric Langlands for l-adic sheaves (1)
Horaire16:00 à 17:30
Diffusion Meeting ID: 975 6850 6098 Passcode: R6ccZ1
RésumeIn celebrated work, Beilinson-Drinfeld formulated a categorical analogue of the Langlands program for unramified automorphic forms. Their conjecture has appeared specialized to the setting of algebraic D-modules: non-holonomic D-modules play a prominent role in known constructions. In these talks, we will translate their work back into a statement suitable for (certain) automorphic functions, refining the Langlands conjectures in this setting. Logically, this proceeds in two steps. First, we will formulate a categorical conjecture suitable in other geometric settings, including l-adic sheaves. Second, we will explain the proof of the trace conjecture, which provides an (unconditional) relationship between automorphic sheaves and automorphic functions. This is joint work with Arinkin, Gaitsgory, Kazhdan, Rozenblyum, and Varshavsky.