# Lectures on modular Deligne--Lusztig theory

## TL;DR

This paper discusses the role of mod-$\,\ell$ cohomology of Deligne--Lusztig varieties in understanding the modular representation theory of finite reductive groups, based on lecture notes from 2016.

## Contribution

It provides an exposition highlighting the significance of mod-$\ell$ cohomology in modular representation theory, with insights from recent lectures.

## Key findings

- Emphasizes the importance of mod-$\ell$ cohomology in modular representation theory.
- Connects geometric methods to algebraic representations of finite groups.
- Provides a pedagogical overview based on recent lectures.

## Abstract

These notes are based on a series of lectures given by the author at the Centre Bernoulli (EPFL) in July 2016. They aim at illustrating the importance of the mod-$\ell$ cohomology of Deligne--Lusztig varieties in the modular representation theory of finite reductive groups.