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The geometric Satake correspondence for ramified groups. (English. French summary) Zbl 1392.11036
Summary: 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.

##### MSC:
 11G18 Arithmetic aspects of modular and Shimura varieties 14G35 Modular and Shimura varieties 20G25 Linear algebraic groups over local fields and their integers
##### Keywords:
geometric Satake; affine flag variety; local models
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