相关论文: On the flatness of models of certain Shimura varie…

Let $R$ be a Henselian DVR with finite residue field. Let $G$ be a finite type, flat $R$-group scheme (not necessarily commutative) with smooth generic fiber. We show that $H^1_{\mathrm{fppf}}(\mathrm{Spec} R,G)$ is finite. We then give an…

This is a largely expository article based on our previous work on arithmetic diagonal cycles on unitary Shimura varieties. We define a class of Shimura varieties closely related to unitary groups which represent a moduli problem of abelian…

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 study the mod $p$-points of the Kisin--Pappas integral models of Shimura varieties of Hodge type with parahoric level. We show that if the group is quasi-split, then every isogeny class contains the reduction of a CM point, proving a…

The special fiber of the local model of a PEL Shimura variety with Iwahori-type level structure admits a cellular decomposition. The set of strata is in a natural way a finite subset of the affine Weyl group determined by the Shimura data.…

Let R be a discrete valuation ring of unequal characteristic which contains a primitive p^2-th root of unity. If K is the fraction field of R, it is well known that (Z/p^2 Z)_K is isomorphic to \mu_{p^2,K}. We prove that any finite and flat…

We give a unified formulation of a mass for arbitrary abelian varieties with PEL-structures and show that it equals a weighted class number of a reductive $\Q$-group $G$ relative to an open compact subgroup $U$ of $G(\A_f)$, or simply…

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…

We prove the Kudla--Rapoport conjecture for Kr\"amer models of unitary Rapoport--Zink spaces at ramified places. It is a precise identity between arithmetic intersection numbers of special cycles on Kr\"amer models and modified derived…

We prove $p$-adic uniformization for Shimura curves attached to the group of unitary similitudes of certain binary skew hermitian spaces $V$ with respect to an arbitrary CM field $K$ with maximal totally real subfield $F$. For a place $v|p$…

In this paper we study the reduction of PEL-Shimura varieties associated to unitary groups of signature (n-1,1) in the inert and unramified case. We describe the Newton polygon and the Ekedahl-Oort stratification. We further study the…

When $p$ is inert in the quadratic imaginary field $E$ and $m<n$, unitary Shimura varieties of signature $(n,m)$ and a hyperspecial level subgroup at $p$, carry a natural foliation of height 1 and rank $m^2$ in the tangent bundle of their…

We prove in this paper a classicality result for overconvergent modular forms on PEL Shimura varieties of type (A) or (C) associated to an unramified reductive group on $\mathbb{Q}_p$. To get this result, we use the analytic continuation…

Kisin and Pappas constructed integral models of Hodge-type Shimura varieties with parahoric level structure at $p>2$, such that the formal neighbourhood of a mod~$p$ point can be interpreted as a deformation space of $p$-divisible group…

Let $F$ be a totally real field, $p$ a prime that we allow to ramify in $F$, and $B$ a quaternion algebra over $F$ which is split at places over $p$. We consider a smooth $p$-adic integral model, the Pappas-Rapoport model, of the…

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 prove that central leaves, Igusa varieties, Newton strata, Kottwitz-Rapoport Strata, Ekedahl-Kottwitz-Oort-Rapoport strata on the special fiber of a Kisin-Pappas integral model of a Hodge-type Shimura variety with connected parahoric…

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 prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic $(0,p)$. As a first application we provide a smooth solution (answer) to a conjecture (question) of…

Let K be a complete field of unequal characteristics $(0,p)$. The aim of this paper is to describe the the semi-stable models for covers $\bold P^1_K@>>>\bold P^1_K$ of degree p, unramified outside $r\leq p$ points and totally ramified…