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Annales scientifiques de l'ENS - Parutions - série 4, 47 (2014)

Parutions < série 4, 47

ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4 47, fascicule 1 (2014)

Thomas Barnet-Lamb, Toby Gee, David Geraghty, Richard Taylor
Local-global compatibility for l=p, II
Annales scientifiques de l'ENS 47, fascicule 1 (2014), 165-179

Télécharger cet article : Fichier PDF

Résumé :
Compatibilité entre les correspondances de Langlands locales aux places divisant l, II
Nous prouvons la compatibilité entre les correspondances de Langlands locale et globale aux places divisant l pour les représentations galoisiennes l-adiques associées à des représentations automorphes cuspidales algébriques régulières de GL _n sur un corps CM ou totalement réel qui sont duales de leur conjuguée complexe à un twist près. Nous prouvons cette compatibilité à semi-simplification près dans tous les cas, et à semi-simplification de Frobenius près lorsque le poids est régulier au sens de Shin.

Mots-clefs : Représentations galoisiennes, représentations automorphes.

Abstract:
We prove the compatibility at places dividing l of the local and global Langlands correspondences for the l-adic Galois representations associated to regular algebraic essentially (conjugate) self-dual cuspidal automorphic representations of GL_n over an imaginary CM or totally real field. We prove this compatibility up to semisimplification in all cases, and up to Frobenius semisimplification in the case of Shin-regular weight.

Keywords: Galois representations, automorphic representations.

Class. math. : 11F33.


ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

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