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arXiv · 1404.6416

Introduction to chtoucas for reductive groups and to the global Langlands parameterization

Vincent Lafforgue
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Abstract

This is a translation in English of version 5 of the article arXiv:1404.3998, which is itself an introduction to arXiv:1209.5352. We explain all the ideas of the proof of the following theorem. 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. 2017-12-24. Introduction to chtoucas for reductive groups and to the global Langlands parameterization. https://arxiv.org/abs/1404.6416

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