Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale

Lafforgue, Vincent

doi:10.1090/jams/897

Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale
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by Vincent Lafforgue;

J. Amer. Math. Soc. 31 (2018), 719-891

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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