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arXiv · 1209.5352

Chtoucas pour les groupes r\'eductifs et param\'etrisation de Langlands globale

Vincent Lafforgue
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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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Vincent Lafforgue. 2012-09-24. Chtoucas pour les groupes r\'eductifs et param\'etrisation de Langlands globale. https://arxiv.org/abs/1209.5352

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