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arXiv · 1805.12231

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

Will Sawin·Nicolas Templier
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Abstract

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.

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Will Sawin, Nicolas Templier. 2020-09-27. On the Ramanujan conjecture for automorphic forms over function fields I. Geometry. https://arxiv.org/abs/1805.12231

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