HU Credits: 2

Degree/Cycle: 2nd degree (Master)

Responsible Department: Mathematics

Semester: 1st Semester

Teaching Languages: Hebrew

Campus: E. Safra

Course/Module Coordinator: Prof Yakov Varshavsky

Coordinator Email: yakov.varshavsky@mail.huji.ac.il

Coordinator Office Hours: by appointment

Teaching Staff:
Prof Yakov Varshavsky

Course/Module description:
The goal of the seminar (jointly delivered with Avraham Aizenbud, Dmitry Gourevitch, Eitan Sayag and David Kazhdan)
"Finiteness for Hecke algebras of p-adic groups" is to describe a recent paper
"Finiteness for Hecke algebras of p-adic groups"
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).

Course/Module aims:
see above

Learning outcomes - On successful completion of this module, students should be able to:
see above

Attendance requirements(%):
100

Teaching arrangement and method of instruction: see above

Course/Module Content:
see above

Required Reading:
see above

Additional Reading Material:
see above

Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 100 %
to be decided

Additional information:
see above