Related papers: Rapoport-Zink spaces for spinor groups

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…

In this article, we give a concrete description of the underlying reduced subscheme of the Rapoport--Zink spaces for spinor similitude groups with special maximal parahoric (and non-hyperspecial) level structure. Moreover, we give two…

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 give a construction of "integral local Shimura varieties" which are formal schemes that generalize the well-known integral models of the Drinfeld $p$-adic upper half spaces. The construction applies to all classical groups, at least for…

We enlarge the class of Rapoport-Zink spaces of Hodge type by modifying the centers of the associated $p$-adic reductive groups. These such-obtained Rapoport-Zink spaces are called of abelian type. The class of Rapoport-Zink spaces of…

This survey article explains the construction of Rapoport-Zink local models and their use in understanding various questions relating to the singularities in the reduction modulo p of certain Shimura varieties with parahoric level structure…

We prove a conjecture of Pappas and Rapoport about the existence of ''canonical'' integral models of Shimura varieties of Hodge type with quasi-parahoric level structure at a prime $p$. For these integral models, we moreover show…

We present a general and comprehensive overview of recent developments in the theory of integral models of Shimura varieties of Hodge type. The paper covers the following topics: construction of integral models, their possible moduli…

We describe the structure of the supersingular Rapoport-Zink space associated to the group of unitary similitudes of signature (2,n-2) for an unramified quadratic extension of p-adic fields. In earlier work, two of the authors described the…

We construct regular integral canonical models for Shimura varieties attached to Spin groups at (possibly ramified) odd primes. We exhibit these models as schemes of 'relative PEL type' over integral canonical models of larger Spin Shimura…

We compute the image of the $p$-adic period map for polarized K3 surfaces with supersingular reduction. This gives rise to a Rapoport-Zink type uniformization of their moduli space by an explicit open rigid analytic subvariety of a local…

We study the basic locus of Shimura varieties associated to the group of spinor similitudes of a quadratic space over $\mathbb{Q}$ with level structure given by the stabilizer of a vertex lattice. We give a description of the underlying…

We prove several results about p-divisible groups and Rapoport-Zink spaces. Our main goal is to prove that Rapoport-Zink spaces at infinite level are naturally perfectoid spaces, and to give a description of these spaces purely in terms of…

We consider unitary Shimura varieties at places where the totally real field ramifies over $\mbQ$. Our first result constructs comparison isomorphisms between absolute and relative local models in this context, which relies on a…

In this paper, we introduce variants of formal nearby cycles for a locally noetherian formal scheme over a complete discrete valuation ring. If the formal scheme is locally algebraizable, then our nearby cycle gives a generalization of…

Let (G, \mu) be a pair of a reductive group G over the p-adic integers and a minuscule cocharacter {\mu} of G defined over an unramified extension. We introduce and study "(G, \mu)-displays" which generalize Zink's Witt vector displays. We…

We compute the level groups associated with mixed Shimura varieties that appear at the boundaries of compactifications of Shimura varieties and show that the boundaries of minimal compactifications of Pappas-Rapoport integral models are…

In this paper, we construct good toroidal and minimal compactifications in the sense of Lan-Stroh for integral models of abelian-type Shimura varieties. We start with finding suitable types of cusp labels and cone decompositions which are…

This is a survey article that advertizes the idea that there should exist a theory of p-adic local analogues of Shimura varieties. Prime examples are the towers of rigid-analytic spaces defined by Rapoport-Zink spaces, and we also review…

The motivation for this paper is the study of arithmetic properties of Shimura varieties, in particular the Newton stratification of the special fiber of a suitable integral model at a prime with parahoric level structure. This is closely…