On the Ramanujan Conjecture for Automorphic Forms over Function Fields

by Prof. Nicolas Templier (Cornell University)

Wednesday Jun 6, 2018, 10:30 AM → 11:30 AM Europe/Paris

Centre de conférences Marilyn et James Simons (IHES)

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 Bun_G, and on trace formulas. Work with Will Sawin.