Fibration de Hitchin et structure endoscopique de la formule des traces

Abstract

The Hitchin fibration is a well suited tool to study the geometric side of the trace formula for Lie algebra from the point of view of moduli spaces of vector bundles over a curve. The endoscopy groups appear naturally when we decompose the cohomology of the Hitchin fibration by its natural symmetries. Following this dictionary, we can formulate a global and geometric version of Langlands–Shelstad’s fundamental lemma. This conjecture has been proved in the case of unitary groups in a joint work with G. Laumon.