Spectral action on isocrystals

Abstract: This is joint work in progress with Dennis Gaitsgory, Alain Genestier and Vincent Lafforgue. Let $G$ be a reductive group over a local function field $F$. In their seminal work, Fargues and Scholze proposed a geometrization of the local Langlands correspondance for the pair $(G,F)$ by constructing a 'spectral action' on the category of $\ell$-adic sheaves on $\mathrm{Bun}_G$, the stack of $G$-torsors on the Fargues-Fontaine curve. The goal of this talk is to explain the construction of a different spectral action on the category of sheaves on the stack of $G$-isocrystals which should offer another geometrization of the local Langlands correspondance. Our construction has the benefit of being naturally compatible with the announced work of Hemo and Zhu and should also be equipped with a strong form of local-global compatibility.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar