Introduction aux chtoucas pour les groupes réductifs et à la paramétrisation de Langlands globale
Abstract
This is an introduction to the article "Chtoucas pour les groupes réductifs et paramétrisation 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2014
- DOI:
- 10.48550/arXiv.1404.3998
- arXiv:
- arXiv:1404.3998
- Bibcode:
- 2014arXiv1404.3998L
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - Representation Theory;
- 14G35;
- 14H60;
- 11F70
- E-Print:
- in French. arXiv admin note: substantial text overlap with arXiv:1209.5352