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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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On the Ramanujan conjecture for automorphic forms over function fields I. Geometry
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by Will Sawin and Nicolas Templier
J. Amer. Math. Soc. 34 (2021), 653-746
Published electronically: April 16, 2021


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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Bibliographic Information
  • Will Sawin
  • Affiliation: ETH Institute for Theoretical Studies, ETH Zurich, 8092 Zürich, Switzerland
  • MR Author ID: 1022068
  • Nicolas Templier
  • Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
  • MR Author ID: 853743
  • Received by editor(s): July 4, 2018
  • Received by editor(s) in revised form: September 5, 2020, and September 27, 2020
  • Published electronically: April 16, 2021
  • Additional Notes: This article begun while both the authors were in residence at the MSRI, supported by the NSF under Grant No. DMS-1440140. The authors received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement no. 290766 (AAMOT) to visit IHES. The first author was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation. The second author was supported by the NSF-CAREER under agreement No. DMS-1454893, and by a Simons Fellowship under agreement 500294.
  • © Copyright 2021 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 34 (2021), 653-746
  • MSC (2020): Primary 14D24, 11F70, 14F20, 22E57, 20G30
  • DOI:
  • MathSciNet review: 4334190