The Geometric Satake Correspondence for Ramified Groups

Abstract

We prove the geometrical 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.

35 pages, with an appendix joint with Timo Richarz. New materials added in Section 6. arXiv admin note: text overlap with arXiv:1012.5979 by other authors