On the Ramanujan Conjecture for Automorphic Forms over Function Fields
by Prof. Nicolas Templier (Cornell University)
at IHES ( Centre de conférences Marilyn et James Simons )
Let G be a reductive group over a function field of large enough characteristic. We prove the temperedness at unramified places of automorphic representations of G, subject to a local assumption at one place, stronger than supercuspidality. Such an assumption is necessary, as was first shown by Saito-Kurokawa and Howe-Piatetskii-Shapiro in the 70's. Our method relies on the l-adic geometry of BunG, and on trace formulas. Work with Will Sawin.
|Organisé par||Ahmed Abbes|