Mod p Hecke algebras and perverse F_p-sheaves

Abstract: We explain a mod $p$ version of the geometric Satake isomorphism which gives a sheaf-theoretic description of the spherical mod $p$ Hecke algebra. We also construct central elements in the Iwahori mod p Hecke algebra by adapting a method due to Gaitsgory. Our proofs rely crucially on the theory of $F$-singularities, and along the way we prove new results about the singularities of affine Schubert varieties. We expect these results to have applications toward a mod $p$ Langlands correspondence.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

Series comments: The Zoom Meeting ID is: 995 3670 1681. The password for the series is: *The first three-digit prime*. Please visit the external homepage for notes and videos from past talks.