Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale

Lafforgue, Vincent¹

¹ CNRS et Institut Fourier, UMR 5582, Université Grenoble Alpes, 100 rue des Maths, 38610 Gières, France

Journal of the American Mathematical Society, Tome 31 (2018) no. 3, pp. 719-891

Résumé

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.

Détail

DOI : 10.1090/jams/897

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