The geometric Satake correspondence for ramified groups
[La correspondance Satake géométrique pour les groupes ramifiés]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 48 (2015) no. 2, pp. 409-451.

Nous démontrons l'isomorphisme de Satake géométrique pour un groupe réductif défini sur F=k((t)) et déployé sur une extension modérément ramifiée. Nous donnons comme application une description des cycles évanescents sur certaines variétés de Shimura via les modèles locaux de Rapoport-Zink-Pappas.

We prove the geometric Satake isomorphism for a reductive group defined over F=k((t)), and split over a tamely ramified extension. As an application, we give a description of the nearby cycles on certain Shimura varieties via the Rapoport-Zink-Pappas local models.

Publié le :
DOI : 10.24033/asens.2248
Classification : 22E57, 14M15, 14G35.
Keywords: Geometric Satake, affine flag variety, local models.
Mot clés : Satake géométrique, variété de drapeaux affine, modèles locaux. 
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     author = {Zhu, Xinwen},
     title = {The geometric {Satake} correspondence  for ramified groups},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {409--451},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 48},
     number = {2},
     year = {2015},
     doi = {10.24033/asens.2248},
     mrnumber = {3346175},
     zbl = {1392.11036},
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Zhu, Xinwen. The geometric Satake correspondence  for ramified groups. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 48 (2015) no. 2, pp. 409-451. doi : 10.24033/asens.2248. http://www.numdam.org/articles/10.24033/asens.2248/

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