Unipotent categorical local Langlands correspondence

Abstract: Following the local geometric Langlands approach, we formulate a categorical form of the local Langlands conjecture using the geometry on a certain infinite dimensional stack classifying F-iscocrystals with additional structure, analogous to a conjecture made by Fargues-Scholze. Using the categorical trace construction we obtain the “unipotent part” of the conjecture from Bezrukavnikov’s equivalence of two realizations of the affine Hecke category. Joint work in progress with Xinwen Zhu.

algebraic geometrynumber theory

Audience: researchers in the topic

Comments: Access code is a(8) where a(n) = 5*a(n-1) + 3 with a(0) = 1.

Séminaire de géométrie arithmétique et motivique (Paris Nord)