Unipotent categorical local Langlands correspondence

Abstract: We formulate a categorical form of the local Langlands conjecture through perfect algebraic 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.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

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