The Geometric Satake Correspondence for Ramified Groups
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.
© 2015 Société Mathématique de France. The author would like to thank D. Gaitsgory, T. Haines, Y. Liu, I. Mirković, G. Pappas, M. Rapoport, T. Richarz, E. Urban, Z. Yun for useful discussions. The author also thanks the hospitality of Tsinghua University, where part of the work is done. The work of the author is supported by the NSF grant under DMS-1001280.
Submitted - 1107.5762v3.pdf
Published - Zhu_2015p409.pdf