Notes on Rapoport--Zink spaces of Hodge type with parahoric level structure

Abstract

In this article, we treat two questions on Rapoport--Zink spaces of Hodge type constructed by Hamacher and Kim. One of which is their singularities, and the other is $p$-adic uniformization of Shimura varieties. More precisely, we prove that the singularity of a Rapoport--Zink space is controlled by its asssociated local model, and the basic locus of a Kisin--Pappas integral model of a Shimura variety is uniformized by the corresponding Rapoport--Zink space. These results extend the known facts by Rapoport and Zink in the case of PEL type.

18 pages, comments are welcome

References in corpus (2)

• Compatibility of certain integral models of Shimura varieties of abelian type
• Rapoport--Zink spaces for spinor groups with special maximal parahoric level structure

Cited by in corpus (1)

• Rapoport--Zink spaces for spinor groups with special maximal parahoric level structure