Local-global compatibility for l=p, II
[Compatibilité entre les correspondances de Langlands locales aux places divisant l, II]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 47 (2014) no. 1, pp. 165-179.

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 GLn 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.

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 GLn 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.

Publié le :
DOI : 10.24033/asens.2212
Classification : 11F33.
Keywords: Galois representations, automorphic representations.
Mot clés : Représentations galoisiennes, représentations automorphes. 
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     author = {Barnet-Lamb, Thomas and Gee, Toby and Geraghty, David and Taylor, Richard},
     title = {Local-global compatibility for~$l=p$, {II}},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {165--179},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 47},
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Barnet-Lamb, Thomas; Gee, Toby; Geraghty, David; Taylor, Richard. Local-global compatibility for $l=p$, II. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 47 (2014) no. 1, pp. 165-179. doi : 10.24033/asens.2212. http://www.numdam.org/articles/10.24033/asens.2212/

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