相关论文: An alternative construction of zip period maps for…

We formulate an integral Frobenius period map for the framed crystalline prismatization of the $p$-integral model $\mathcal{S}$ of a Shimura variety with good reduction. By analyzing reductions of this map, we derive a period map from the…

Let $Y$ be a subvariety contained in a smooth Mumford compactification of an orthogonal Shimura variety $M \subset A_g$, where $A_g$ is the moduli space of principally polarized abelian varieties of dimension $g$ with some level structure,…

We study the Hodge-Tate period domain associated to a quaternionic Shimura curve at a prime of bad reduction, and give an explicit description of its Ekedahl-Oort stratification.

We study the Ekedahl-Oort stratification for good reductions of Shimura varieties of PEL type. These generalize the Ekedahl-Oort strata defined and studied by Oort for the moduli space of principally polarized abelian varieties (the "Siegel…

Let $(\mathsf{G},\mathsf{X})$ be a Shimura datum of Hodge type. Let $p$ be an odd prime such that $\mathsf{G}_{\mathbb{Q}_p}$ splits after a tamely ramified extension and $p\nmid |\pi_1(\mathsf{G}^{\rm der})|$. Under some mild additional…

We define and study the Hodge stratification for the special fiber of Shimura varieties defined with the Pappas-Rapoport condition, in the case of low ramification index ($e \leq 3$). For $e \leq 2$, the Hodge polygon induces a strong…

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…

Let $F$ be a real quadratic field in which a fixed prime $p$ is inert, and $E_0$ be an imaginary quadratic field in which $p$ splits; put $E=E_0 F$. Let ${{\rm Sh}}_{1,n-1}$ be the special fiber over $\mathbb{F}_{p^2}$ of the Shimura…

We reinterpret and generalize the construction of local Shimura varieties and their non-minuscule analogs by viewing them as moduli spaces of admissible pairs. Our main application is a bi-analytic Ax-Lindemann theorem comparing, in the…

The main result of this paper is the existence of Galois representations associated with the mod $p$ (or mod $p^m$) cohomology of the locally symmetric spaces for $\GL_n$ over a totally real or CM field, proving conjectures of Ash and…

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 develop local cohomology techniques to study the finite slope part of the coherent cohomology of Shimura varieties. The local cohomology groups we consider are a generalization of overconvergent modular forms, and they are defined by…

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…

We construct universal $G$-zips on good reductions of the Pappas-Rapoport splitting models for PEL-type Shimura varieties. We study the induced Ekedahl-Oort stratification, which sheds new light on the mod $p$ geometry of splitting models.…

In this paper we study the geometry of the special fiber of Pappas-Rapoport models of Shimura varieties in the Hilbert case. More precisely we prove that the stratification induced by the Hodge polygon is a good stratification, which is…

We study a period map for triple coverings of $\mathbf P^2$branching along special configurations of $6$ lines. Though the moduli space of special configurations isa two dimensional variety,the minimal models of the coverings form a…

The goal of this paper is to show that the cohomology of compact unitary Shimura varieties is concentrated in the middle degree and torsion-free, after localizing at a maximal ideal of the Hecke algebra satisfying a suitable genericity…

We determine the irreducible components of Igusa varieties for Shimura varieties of Hodge type under a mild condition and use that to compute the irreducible components of central leaves. In particular, we show that a strong version of the…

We introduce the theory of inscribed $v$-sheaves, a differentiable extension of the theory of diamonds and $v$-sheaves with internal tangent bundles that are often relative inscribed Banach-Colmez spaces, then apply this theory to the study…

We prove that Shimura varieties and geometric period images satisfy a $p$-adic extension property for large enough primes $p$. More precisely, let $\mathsf{D}^{\times}\subset \mathsf{D}$ denote the inclusion of the closed punctured unit…