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Journal of the American Mathematical Society

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Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale


Author: Vincent Lafforgue
Journal: J. Amer. Math. Soc. 31 (2018), 719-891
MSC (2010): Primary 14G35, 14H60, 11F70
DOI: https://doi.org/10.1090/jams/897
Published electronically: February 23, 2018
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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.


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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

DOI: https://doi.org/10.1090/jams/897
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
Article copyright: © Copyright 2018 American Mathematical Society

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