Le lemme fondamental pond\'er\'e. II. \'Enonc\'es cohomologiques

TL;DR

This paper extends Ngô's theorems on the cohomology of the Hitchin fibration, leading to a proof of Arthur's weighted fundamental lemma, advancing understanding in geometric representation theory.

Contribution

It generalizes Ngô's main results to the truncated Hitchin fibration and proves Arthur's weighted fundamental lemma.

Findings

Extended Ngô's theorems to truncated Hitchin fibration

Proved Arthur's weighted fundamental lemma

Enhanced understanding of cohomology in geometric representation theory

Abstract

In this paper, we study the cohomology of the truncated Hitchin fibration, which was introduced in a previous paper. We extend Ng\^o's main theorems on the cohomology of the elliptic part of the Hitchin fibration. As a consequence, we get a proof of Arthur's weighted fundamental lemma