Kazhdan seminar, Aizenbud, Gourevitch, Sayag, Varshavsky "Finiteness for Hecke algebras of p-adic groups"

Sun, 23/10/202214:00-16:00
Ross 70 and Zoom

This is Kazhdan Sunday seminar, which will be run by Abraham Aizenbud, Dmitry Gurevich, Eitan Sayag and Yakov Varshavsky and appears as 80853 in shnaton.

The zoom link is 


The website for the seminar is 


(supposed to be open to everyone) and all the information (including zoom links, slides and recordings) will be placed there. 

Slides for the first lecture: 


Abstract: The goal of this seminar is to describe a recent paper https://arxiv.org/abs/2203.04929
by Jean-Francois Dat, David Helm, Robert Kurinczuk, Gilbert Moss.

Let G be a reductive group over a non-archimedean local field F of
residue characteristic p. The main goal is to prove that the Hecke
algebras of G(F) with coefficients in a Z_l-algebra R for l not equal
to p are finitely generated modules over their centers, and that these
centers are finitely generated R-algebras. Following Bernstein's
original strategy, we will then deduce that "second adjointness" holds
for smooth representations of G(F) with coefficients in any ring R in
which p is invertible. These results had been conjectured for a long
time. The crucial new tool that unlocks the problem is the
Fargues-Scholze morphism between a certain ``excursion algebra"
defined on the Langlands parameters side and the Bernstein center of

First lecture: Rami Eisenbud "Overview"