Nous prouvons la compatibilité entre les correspondances de Langlands locale et globale aux places divisant pour les représentations galoisiennes -adiques associèes à des représentations automorphes cuspidales algébriques et régulières de 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 et ont un poids régulier au sens de Shin.
We prove the compatibility of the local and global Langlands correspondences at places dividing for the -adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations of over an imaginary CM field, under the assumption that the automorphic representations have Iwahori-fixed vectors at places dividing and have Shin-regular weight.
@article{AFST_2012_6_21_1_57_0,
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},
number = {1},
year = {2012},
doi = {10.5802/afst.1329},
zbl = {1259.11057},
mrnumber = {2954105},
language = {en},
url = {http://www.numdam.org/articles/10.5802/afst.1329/}
}
TY - JOUR AU - Barnet-Lamb, Thomas AU - Gee, Toby AU - Geraghty, David AU - Taylor, Richard TI - Local-global compatibility for $l=p$, I JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2012 SP - 57 EP - 92 VL - 21 IS - 1 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1329/ DO - 10.5802/afst.1329 LA - en ID - AFST_2012_6_21_1_57_0 ER -
%0 Journal Article %A Barnet-Lamb, Thomas %A Gee, Toby %A Geraghty, David %A Taylor, Richard %T Local-global compatibility for $l=p$, I %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2012 %P 57-92 %V 21 %N 1 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://www.numdam.org/articles/10.5802/afst.1329/ %R 10.5802/afst.1329 %G en %F AFST_2012_6_21_1_57_0
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://www.numdam.org/articles/10.5802/afst.1329/
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