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Annales scientifiques de l'ENS - Titles - série 4, 51 (2018)

Titles < série 4, 51

ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4 51, fascicule 4 (2018)

Peter Scholze
On the p-adic cohomology of the Lubin-Tate tower with an appendix «Accessible and weakly accessible period domains» by Michael Rapoport
Annales scientifiques de l'ENS 51, fascicule 4 (2018), 811-863

Télécharger cet article : Fichier PDF

Résumé :
Sur la cohomologie p-adique de la tour de Lubin-Tate avec un appendice «Accessible and weakly accessible period domains» par Michael Rapoport
Nous prouvons un résultat de finitude pour la cohomologie p-adique de la tour de Lubin-Tate. Pour tout n1 et corps p-adique F, cela fournit un functor canonique à partir de représentations p-adiques admissibles de GL _n(F) vers des représentations p-adiques admissibles de Gal _FD^, où Gal _F est le groupe de Galois absolu de F, et D/F est l'algèbre à division centrale d'invariant 1/n. De plus, nous vérifions une compatibilité locale-globale pour cette correspondance, et une compatibilité avec le patching de Caraiani-Emerton-Gee-Geraghty-Paskunas-Shin.

Mots-clefs : Tour de Lubin-Tate, cohomologie p-adique, correspondance de Langlands, patching, compatibilité local-global, courbes de Shimura.

Abstract:
We prove a finiteness result for the p-adic cohomology of the Lubin-Tate tower. For any n1 and p-adic field F, this provides a canonical functor from admissible p-adic representations of GL _n(F) towards admissible p-adic representations of Gal _FD^, where Gal _F is the absolute Galois group of F, and D/F is the central division algebra of invariant 1/n. Moreover, we verify a local-global-compatibility statement for this correspondence, and compatibility with the patching construction of Caraiani-Emerton-Gee-Geraghty-Paskunas-Shin.

Keywords: Lubin-Tate tower, p-adic cohomology, Langlands correspondence, patching, local-global compatibility, Shimura curves.

Class. math. : 14G22, 11S37, 11F80, 11F85.


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

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