English

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

Algebraic Geometry 2018-01-11 v9 Representation Theory

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.

Keywords

Cite

@article{arxiv.1209.5352,
  title  = {Chtoucas pour les groupes r\'eductifs et param\'etrisation de Langlands globale},
  author = {Vincent Lafforgue},
  journal= {arXiv preprint arXiv:1209.5352},
  year   = {2018}
}

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