## Number Theory Seminar: Elmar Grosse-Klöne

- Date: 03/30/2017
- Time: 15:30

University of British Columbia

Supersingular Hecke modules for {\rm GL}_n(F) and (\psi,\Gamma)-modules

Let F be a finite extension field of {\mathbb Q}_p. Let {\mathcal H}

be the pro-p-Iwahori-Hecke algebra for {\rm GL}_n(F), with

coefficients in the residue field k of {\mathcal O}_F (or a finite

extension of it). We are going to discuss an exact functor D from the

category of supersingular {\mathcal H}-modules to the category of

(\psi,\Gamma)-modules over k((X)). The latter category generalizes in

a straightforward way the one defined and studied by Colmez in the case F={\mathbb Q}_p; in particular, it admits an exact functor to the category of (\varphi,\Gamma)-modules, and hence to that of Galois representations. Our main result today is that the functor D is almost fully faithful, i.e. it is fully faithful when restricted to the category of supersingular {\mathcal H}-modules satisfying a very mild additional assumption.

This event is part of the PIMS Focus Group on Representations in Arithmetic.

Location: ESB 4127