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

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.

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.

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     author = {Barnet-Lamb, Thomas and Gee, Toby and Geraghty, David and Taylor, Richard},
     title = {Local-global compatibility for $l=p$, {I}},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {57--92},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 21},
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     year = {2012},
     doi = {10.5802/afst.1329},
     mrnumber = {2954105},
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     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/afst.1329/}
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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, Série 6, Tome 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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