Un th\'eor\`eme du support pour la fibration de Hitchin

TL;DR

This paper extends Ngô Bao Châu's support theorem for the Hitchin fibration, showing that the relative cohomology is determined by its restriction to any dense open subset, now including the entire Hitchin fibration and the global nilpotent cone.

Contribution

It generalizes the support theorem for the Hitchin fibration to include the entire fibration and the global nilpotent cone, beyond the elliptic part.

Findings

Support theorem extended to the whole Hitchin fibration

Includes the global nilpotent cone in the analysis

Cohomology determined by restriction to dense open subsets

Abstract

The main tool in Ng\^o Bao Ch\^au's proof of the Langlands-Shelstad fundamental lemma, is a theorem on the support of the relative cohomology of the elliptic part of the Hitchin fibration. For GL(n) and a divisor of degree >2g-2, the theorem says that the relative cohomology is completely determined by its restriction to any dense open subset of the base of the Hitchin fibration. In this note we would like to present in this particular case, our extension of that theorem to the whole Hitchin fibration, including the global nilpotent cone.