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arXiv · 2012.07076

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

Yasuhiro Oki
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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.

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Yasuhiro Oki. 2020-12-13. Notes on Rapoport--Zink spaces of Hodge type with parahoric level structure. https://arxiv.org/abs/2012.07076

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