Introduction aux chtoucas pour les groupes r\'eductifs et \`a la param\'etrisation de Langlands globale

Vincent Lafforgue

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arXiv · 1404.3998

Introduction aux chtoucas pour les groupes r\'eductifs et \`a la param\'etrisation de Langlands globale

Vincent Lafforgue

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Abstract

This is an introduction to the article "Chtoucas pour les groupes r\'eductifs et param\'etrisation de Langlands globale", arXiv:1209.5352. We explain all the ideas of the proof. 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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BibTeX RIS

Vincent Lafforgue. 2014-04-15. Introduction aux chtoucas pour les groupes r\'eductifs et \`a la param\'etrisation de Langlands globale. https://arxiv.org/abs/1404.3998

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