Zhu, Xinwen The geometric Satake correspondence for ramified groups. (English. French summary) Zbl 1392.11036 Ann. Sci. Éc. Norm. Supér. (4) 48, No. 2, 409-451 (2015). 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. Cited in 2 ReviewsCited in 14 Documents 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 PDF BibTeX XML Cite \textit{X. Zhu}, Ann. Sci. Éc. Norm. Supér. (4) 48, No. 2, 409--451 (2015; Zbl 1392.11036) Full Text: DOI Link arXiv