A geometric construction of central elements in affine mod $p$ Hecke algebras

Abstract: Let $G$ be a split connected reductive group over a local field of positive characteristic. In the case of characteristic zero coefficients, Gaitsgory gave a geometric construction of central elements in the affine Hecke algebra of $G$ by applying a nearby cycles functor on a Beilinson-Drinfeld affine Grassmannian. In this talk I will explain how to do an analogous construction for the affine mod $p$ Hecke algebra of $G$. Our techniques combine the geometry of Gaitsgory's construction (and simplifications due to Zhu) with perverse mod $p$ sheaves and tools from $F$-singularities.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar