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

2018/05/30 by Will Sawin, Sawin, Will, Nicolas Templier +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1805.12231

openalex publication_date 2018/05/30 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let G be a split semisimple group over a function field. We prove the\ntemperedness at unramified places of automorphic representations of G,\nsubject to a local assumption at one place, stronger than supercuspidality, and\nassuming the existence of cyclic base change with good properties. Our method\nrelies on the geometry of \Bun_G. It is independent of the work\nof Lafforgue on the global Langlands correspondence.\n

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