On the Ramanujan conjecture for automorphic forms over function fields I. Geometry

Let $G$ be a split semisimple group over a function field. We prove the temperedness at unramified places of automorphic representations of $G$, subject to a local assumption at one place, stronger than supercuspidality, and assuming the existence of cyclic base change with good properties. Our meth...

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Bibliographic Details
Main Authors Sawin, Will, Templier, Nicolas
Format Journal Article
LanguageEnglish
Published 30.05.2018
Subjects
Mathematics - Algebraic Geometry
Mathematics - Number Theory
Mathematics - Representation Theory
Online AccessGet full text
DOI10.48550/arxiv.1805.12231

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Summary:Let $G$ be a split semisimple group over a function field. We prove the temperedness at unramified places of automorphic representations of $G$, subject to a local assumption at one place, stronger than supercuspidality, and assuming the existence of cyclic base change with good properties. Our method relies on the geometry of $\operatorname{Bun}_G$. It is independent of the work of Lafforgue on the global Langlands correspondence.
DOI:10.48550/arxiv.1805.12231