On the geometric fundamental lemma of Kottwitz

TL;DR

This paper provides a proof of the geometric fundamental lemma of Kottwitz, which is crucial for establishing the fundamental lemma for unitary groups, a key component in the Langlands program.

Contribution

The paper offers a rigorous proof of the geometric fundamental lemma, advancing the understanding of fundamental lemmas in the context of automorphic forms and representation theory.

Findings

Proof of the geometric fundamental lemma of Kottwitz.

Implication for the fundamental lemma of unitary groups.

Progress towards the Langlands program.

Abstract

We give a proof of the geometric fundamental lemma of Kottwitz. As explained by Laumon, this implies the fundamental lemma for the unitary groups.