A support theorem for the Hitchin fibration

Topology of Algebraic Varieties
Topic:A support theorem for the Hitchin fibration
Speaker:Pierre-Henri Chaudouard
Affiliation:Université Paris 7; von Neumann Fellow, School of Mathematics
Date:Tuesday, December 9
Time/Room:2:00pm - 3:30pm/S-101
Video Link:http://video.ias.edu/tav/2014/1209-PierreHenriChaudouard

The main tool in NgĂ´'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 $\mathrm{GL}(n)$ 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 talk, we will explain our extension of that theorem to the whole Hitchin fibration, including the global nilpotent cone (for $\mathrm{GL}(n)$ and a divisor of degree $> 2g-2$). (based on a joint work with G. Laumon).