# Abstract Pierre-Henri Chaudouard

**Pierre-Henri Chaudouard **will speak on

** A support theorem for the Hitchin fibration **

**Abstract:** The main tool in Ngô Bao Châu's proof of the Langlands-Shelstad fundamental lemma, is a support theorem for the relative cohomology of the elliptic part of the Hitchin fibration. For GL(n) and a divisor of degree >2g-2, the support 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 talk, based on a joint work with Gérard Laumon, we will explain that the support theorem extends to the whole Hitchin fibration, including the global nilpotent cone.