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Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo

On the Ramanujan Conjecture for Automorphic Forms over Function Fields

by Prof. Nicolas Templier (Cornell University)

mercredi 6 juin 2018 de au (Europe/Paris)
at IHES ( Centre de conférences Marilyn et James Simons )
Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

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
Contact Email: cecile@ihes.fr