A geometric interpretation of the nilpotent part of local Langlands correspondence modulo l

TL;DR

This paper offers a geometric perspective on Vigneras' mod l Langlands correspondence for p-adic fields by analyzing the mod l cohomology of the Lubin-Tate tower and a Lefschetz operator, under specific congruence conditions.

Contribution

It introduces a novel geometric interpretation of the nilpotent part of the local Langlands correspondence modulo l using cohomological methods.

Findings

Provides a geometric framework linking cohomology and Langlands correspondence

Establishes a connection between the Lubin-Tate tower and mod l representations

Highlights the role of a Lefschetz operator in this geometric interpretation

Abstract

Let p and l be two distinct primes. We show how, under a certain congruence hypothesis, the mod l cohomology of the Lubin-Tate tower together with a certain Lefschetz operator provides a geometric interpretation of Vigneras' Langlands correspondence for a p-adic field with mod l coefficients.