相关论文: On the Bruhat-Tits stratification for GU(2,2) type…
We study the structure of the supersingular locus of the Rapoport--Zink integral model of the Shimura variety for $\mathrm{GU}(2,2)$ over a ramified odd prime with the special maximal parahoric level. We prove that the supersingular locus…
We analyze the geometry of the supersingular locus of the reduction modulo p of a Shimura variety associated to a unitary similitude group GU(1,n-1) over Q, in the case that p is ramified. We define a stratification of this locus and show…
We describe the supersingular locus of a GU(2,2) Shimura variety at a prime inert in the corresponding quadratic imaginary field.
In this note we study the special fiber of the Rapoport-Zink space attached to a quaternionic unitary group. The special fiber is described using the so called Bruhat-Tits stratification and is intimately related to the Bruhat-Tits building…
We describe the structure of the supersingular locus of a Shimura variety for a quaternionic unitary similitude group of degree $2$ over a ramified odd prime $p$ if the level at $p$ is given by a special maximal compact open subgroup. More…
We complete the study of the supersingular locus in the fiber at $p$ of a Shimura variety attached to a unitary similitude group $\GU(1,n-1)$ over $\QQ$ in the case that $p$ is inert. This was started by the first author in \cite{Vo_Uni}…
In this work, we study the supersingular locus of the Shimura variety associated to the unitary group $\mathrm{GU}(2,4)$ over a ramified prime. We show that the associated Rapoport-Zink space is flat, and we give an explicit description of…
In this paper we study the supersingular locus of the reduction modulo p of the Shimura variety for GU(1,s) in the case of an inert prime p. Using Dieudonn\'e theory we define a stratification of the corresponding moduli space of…
We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to $\mathrm{GU}(2,n-2)$. More concretely, we decompose the supersingular locus into a disjoint union of iterated fibrations over (classical)…
We give a description of the $\mathrm{GL}_4$ Rapoport-Zink space, including the connected components, irreducible components, intersection behavior of the irreducible components, and Ekedahl-Oort stratification. As an application of this,…
In this paper, we study the cohomology of the ramified PEL unitary Rapoport-Zink space of signature $(1,n-1)$ by using the Bruhat-Tits stratification on its special fiber. As such, we apply the same method that we developped for the…
We construct the Bruhat--Tits stratification of the reduced locus of the ramified unitary Rapoport--Zink space of signature $(n-1,1)$, with the level being the stabilizer of a vertex lattice. We develop the local model theory for…
In this paper, we describe a stratification on the reduced special fiber of the basic unramified unitary Rapoport-Zink space of signature $(1,n-1)$ and at arbitrary parahoric level. We prove the smoothness, irreducibility and compute the…
We construct the Bruhat-Tits stratification of the reduced basic locus of regular ramified unitary Rapoport-Zink spaces of signature $(n\!-\!1,1)$ at vertex-stabilizer level. To study the Bruhat-Tits strata, we introduce strata…
In this paper, we study the cohomology of the unitary unramified PEL Rapoport-Zink space of signature $(1,n-1)$ at maximal level. Our method revolves around the spectral sequence associated to the open cover by the analytical tubes of the…
We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to $\mathrm{GU}(2,n-2)$. More concretely, we realize irreducible components of the supersingular locus as closed subschemes of flag schemes…
In this paper, we study special cycles on the basic locus of certain unitary Shimura varieties over the ramified primes and their local analogues on the corresponding Rapoport-Zink spaces. We study the support and compute the dimension 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…
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…
In this paper, we study the basic locus in the fiber at $p$ of a certain unitary Shimura variety with a certain parahoric level structure. The basic locus $\widehat{\mathcal{M}^{ss}}$ is uniformized by a formal scheme $\mathcal{N}$ which is…