Types modulo $\ell$ pour les formes int\'erieures de $GL_n$ sur un corps local non archim\'edien

TL;DR

This paper develops a theory of l-modular types for the group GL(m,D) over a non-Archimedean local field, aiding the study of its smooth representations in modular settings.

Contribution

It introduces a new framework for l-modular types for inner forms of GL_n over non-Archimedean fields, extending representation theory tools.

Findings

Established a classification of l-modular types for GL(m,D)

Provided foundational results for studying l-modular smooth representations

Extended existing theories to inner forms of GL_n

Abstract

Let F be a non-Archimedean locally compact field of residue characteristic p, let D be a finite dimensional central division F-algebra and let l be a prime number different from p. We develop a theory of l-modular types for the group GL(m,D), m\>1, in preparation of the study of the l-modular smooth representations of this group.