A mod p geometric Satake isomorphism

Abstract: We apply methods from geometric representation theory toward the mod p Langlands program. More specifically, we explain a mod p version of the geometric Satake isomorphism, which gives a sheaf-theoretic description of the spherical mod p Hecke algebra. In our setup the mod p Satake category is not controlled by the dual group but rather a certain affine monoid scheme. Along the way we will discuss some new results about the F-singularities of affine Schubert varieties. Time permitting, we will explain how to geometrically construct central elements in the Iwahori mod p Hecke algebra by adapting a method due to Gaitsgory.

number theory

Audience: researchers in the topic

Harvard number theory seminar