Related papers: Arithmetic level raising theorem for some unitary …
For an odd prime p, we construct integral models over p for Shimura varieties with parahoric level structure, attached to Shimura data (G,X) of abelian type, such that G splits over a tamely ramified extension of Q_p. The local structure of…
We provide a moduli description of the ramified unitary local model of signature $(n-1,1)$ with arbitrary parahoric level structure, assuming the residue field has characteristic not equal to $2$, thereby confirming a conjecture of…
In this note, we study Shimura varieties for the groups $\mathrm{GU}(V)$, where $V$ is a Hermitian space relative to a CM extension $E/E^+$. We give a description of the supersingular locus of the fiber at a prime $\nu$ over $p$ of such a…
We construct explicit generating series of arithmetic extensions of Kudla's special divisors on integral models of unitary Shimura varieties over CM fields with arbitrary split levels and prove that they are modular forms valued in the…
We consider Shimura varieties associated to a unitary group of signature $(n-s,s)$ where $n$ is even. For these varieties, by using the spin splitting models from Zachos-Zhao, we construct flat, Cohen-Macaulay, and normal $p$-adic integral…
We study integral models of some Shimura varieties with bad reduction at a prime $p$, namely the Siegel modular variety and Shimura varieties associated with some unitary groups. We focus on the case where the level structure at $p$ is…
The goal of this paper is to prove a formula expressing the modular height of a unitary Shimura variety over a CM number field in terms of the logarithm derivative of the Hecke L-function associated with the CM extension. In a more specific…
We study $p$-adic integral models of certain PEL Shimura varieties with level subgroup at $p$ related to the $\Gamma_1(p)$-level subgroup in the case of modular curves. We will consider two cases: the case of Shimura varieties associated…
Consider a PEL-Shimura variety associated to a unitary group that splits over an unramified extension of Q_p. Rapoport and Zink have defined a model of the Shimura variety over the ring of integers of the completion of the reflex field at a…
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 study integral models, so-called Pappas-Rapoport or splitting models, of some PEL Shimura Varieties whose data are ramified at a prime p. We show that except in a specific case, these models are smooth when there is no level at p, and we…
In this paper, we consider the geometric special fibers of local models of Shimura varieties and of moduli of $\bG$-Shtukas with parahoric level structure. We investigate two problems with respect to the irreducibility of local models.…
In this paper we study the geometry of reduction modulo $p$ of the Kisin-Pappas integral models for certain Shimura varieties of abelian type with parahoric level structure. We give some direct and geometric constructions for the EKOR…
The supersingular locus in the fiber at p of a Shimura variety attached to a unitary similitude group GU(1,n-1) over Q is uniformized by a formal scheme \Cal N. In the case when p is inert, we define special cycles Z(x) in \Cal N,…
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.…
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 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…
This is a revised version of a part of the author's preprint "On p-adic uniformization of fake projective planes" (preprint, Max-Planck-Institut fuer Mathematik, 1998 (121)). In this paper we construct explicitly a Shimura surface of…
Given a Hecke eigenform $f$ of weight $2$ and square-free level $N$, by the work of Kohnen, there is a unique weight $3/2$ modular form of level $4N$ mapping to $f$ under the Shimura correspondence. Furthermore, by the work of Waldspurger…
We describe the supersingular locus of a GU(2,2) Shimura variety at a prime inert in the corresponding quadratic imaginary field.