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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 pure and applied mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale
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by Vincent Lafforgue HTML | PDF
J. Amer. Math. Soc. 31 (2018), 719-891 Request permission

Abstract:

For any reductive group $G$ over a global function field, we use the cohomology of $G$-shtukas with multiple modifications and the geometric Satake equivalence to prove the global Langlands correspondence for $G$ in the “automorphic to Galois” direction. Moreover we obtain a canonical decomposition of the spaces of cuspidal automorphic forms indexed by global Langlands parameters. The proof does not rely at all on the Arthur-Selberg trace formula.
References
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Additional Information
  • Vincent Lafforgue
  • Affiliation: CNRS et Institut Fourier, UMR 5582, Université Grenoble Alpes, 100 rue des Maths, 38610 Gières, France
  • Email: vlafforg@math.cnrs.fr
  • Received by editor(s): December 13, 2012
  • Received by editor(s) in revised form: October 15, 2013, September 19, 2015, August 11, 2017, December 20, 2017, and January 5, 2018
  • Published electronically: February 23, 2018
  • Additional Notes: L’auteur fait partie de l’ANR-13-BS01-0001-01
  • © Copyright 2018 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 31 (2018), 719-891
  • MSC (2010): Primary 14G35, 14H60, 11F70
  • DOI: https://doi.org/10.1090/jams/897
  • MathSciNet review: 3787407