Notes on modular representations of $p$-adic groups, and the Langlands correspondence

TL;DR

This paper provides an overview of modular representations of finite groups of Lie type and p-adic groups, along with the modular Langlands correspondence, through expanded lecture notes with examples.

Contribution

It offers a comprehensive exposition on modular representations and the modular Langlands correspondence, including detailed examples and insights.

Findings

Clarifies the structure of modular representations of p-adic groups

Illustrates the modular Langlands correspondence with examples

Provides foundational overview for further research

Abstract

These are expanded notes of some lectures given by the author for a workshop held at the Indian Statistical Institute, Bangalore in June, 2010, giving an exposition on the modular representations of finite groups of Lie type and $p$-adic groups, and the modular Langlands correspondence. These notes give an overview of the subject with several examples.