Rapoport-Zink spaces of Hodge type

Abstract

When $p>2$, we construct a Hodge-type analogue of Rapoport-Zink spaces under the unramifiedness assumption, as formal schemes parametrising "deformations" (up to quasi-isogeny) of $p$-divisible groups with certain crystalline Tate tensors. We also define natural rigid analytic towers with expected extra structure, providing more examples of "local Shimura varieties" conjectured by Rapoport and Viehmann.

79 pages, Section 5 was rewritten

References in corpus (3)

• A guide to the reduction modulo p of Shimura varieties
• Towards a theory of local Shimura varieties
• Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I

Cited by in corpus (7)

• Towards a theory of local Shimura varieties
• Rapoport-Zink spaces for spinor groups
• Affine Grassmannians and the geometric Satake in mixed characteristic
• On the Hodge-Newton filtration for p-divisible groups of Hodge type
• On the Newton stratification in the good reduction of Shimura varieties
• Construction of a Rapoport-Zink space for $\mathrm{GU}(1,1)$ in the ramified $2$-adic case
• On central leaves of Hodge-type Shimura varieties with parahoric level structure