Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo
On the Ramanujan Conjecture for Automorphic Forms over Function Fields
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Europe/Paris
Centre de conférences Marilyn et James Simons (IHES)
Centre de conférences Marilyn et James Simons
IHES
Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette
Description
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.
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