Local-global compatibility for l=p, I
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 21 (2012) no. 1, pp. 57-92.

We prove the compatibility of the local and global Langlands correspondences at places dividing l for the l-adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations of GL n over an imaginary CM field, under the assumption that the automorphic representations have Iwahori-fixed vectors at places dividing l and have Shin-regular weight.

Nous prouvons la compatibilité entre les correspondances de Langlands locale et globale aux places divisant l pour les représentations galoisiennes l-adiques associèes à des représentations automorphes cuspidales algébriques et régulières de GL n sur un corps CM qui sont duales de leur conjuguée complexe, sous les hypothèses supplémentaires que ces représentations automorphes ont des vecteurs fixes par un sous-groupe d’Iwahori aux places divisant l et ont un poids régulier au sens de Shin.

DOI: 10.5802/afst.1329
Barnet-Lamb, Thomas 1; Gee, Toby 2; Geraghty, David 3; Taylor, Richard 4

1 Department of Mathematics, Brandeis University
2 Department of Mathematics, Northwestern University
3 Princeton University and Institute for Advanced Study
4 Department of Mathematics, Harvard University
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Barnet-Lamb, Thomas; Gee, Toby; Geraghty, David; Taylor, Richard. Local-global compatibility for $l=p$, I. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 21 (2012) no. 1, pp. 57-92. doi : 10.5802/afst.1329. http://archive.numdam.org/articles/10.5802/afst.1329/

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