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

Date:
Sun, 23/10/202214:00-16:00
Location:
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.

https://huji.zoom.us/j/82677114374?pwd=RnZUS3EvODBYYVNHaitvZi9iRzBVdz09

The website for the seminar is

https://moodle2.cs.huji.ac.il/nu22/course/view.php?id=80853

(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:

https://moodle2.cs.huji.ac.il/nu22/pluginfile.php/272977/mod_resource/content/0/Lecture%201%20-%20Rami.pdf

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
G(F).

First lecture: Rami Eisenbud "Overview"