相关论文: Potentially good reduction loci of Shimura varieti…
We prove finiteness results for sets of varieties over number fields with good reduction outside a given finite set of places using cyclic covers. We obtain a version of the Shafarevich conjecture for weighted projective surfaces, double…
We survey the theory of local models of Shimura varieties. In particular, we discuss their definition and illustrate it by examples. We give an overview of the results on their geometry and combinatorics obtained in the last 15 years. We…
In this article we prove several level lowering results for cuspidal automorphic representations occurring in the cohomology of the Siegel modular threefold with paramodular level structure by adapting a method of Ribet in his proof of the…
In this paper, we seek an appropriate definition for a Shimura curve of Hodge type in positive characteristics, i.e. a characterization, in terms of geometry mod p, of curves in positive characteristics which are reduction of Shimura curves…
We show that up to potential isogeny, there are only finitely many abelian varieties of dimension $d$ defined over a number field $K$, such that for any finite place $v$ outside a fixed finite set $S$ of places of $K$ containing the…
We give a good reduction criterion for proper polycurves with sections,i.e., successive extensions of family of curves with section, under mild assumption. This criterion is a higher dimensional version of the good reduction criterion for…
Under simplifying hypotheses we prove a relation between the l-adic cohomology of the basic stratum of a Shimura variety of PEL-type modulo a prime of good reduction of the reflex field and the cohomology of the complex Shimura variety. In…
We determine the Galois representations inside the $l$-adic cohomology of some quaternionic and related unitary Shimura varieties at ramified places. The main results generalize the previous works of Reimann and Kottwitz in this setting to…
We propose a model-theoretic structure for Shimura varieties and give necessary and sufficient conditions to obtain categoricity. We show that these conditions are directly related to important conjectures in number theory coming from…
Applying the main results of math.AG/0408295, we identify the motives occurring as cones in the co-localization and localization filtrations of the boundary motive of a Shimura variety.
In this note, we study the superspecial loci of orthogonal type Shimura varieties of signature (n-2, 2) with n>3. We prove a conjecture of Gross on the parametrizations of the superspecial locus in the special fiber of an orthogonal type…
In this paper, we study the $\mu$-ordinary locus of a Shimura variety with parahoric level structure. Under the axioms in \cite{HR}, we show that $\mu$-ordinary locus is a union of some maximal Ekedahl-Kottwitz-Oort-Rapoport strata…
We bound the length of the periodic part of the orbit of a preperiodic rational subvariety via good reduction information. This bound depends only on the degree of the map, the degree of the subvariety, the dimension of the projective…
The reductions of an ideal $I$ give a natural pathway to the properties of $I$, with the advantage of having fewer generators. In this paper we primarily focus on a conjecture about the reduction exponent of links of a broad class of…
We obtain necessary and sufficient conditions for abelian varieties to acquire semistable reduction over fields of low degree. Our criteria are expressed in terms of torsion points of small order defined over unramified extensions.
We show the existence of two new Shimura subvarieties of $\mathcal{A}_2, \mathcal{A}_3$ generically contained in the Torelli locus. They provide the first examples of Shimura subvarieties obtained by means of Jacobians carrying non-trivial…
We seek an appropriate definition for a Shimura curve of Hodge type in positive characteristics via characterizing curves in positive characteristics which are reduction of Shimura curve over $\mathbb{C}$. In this paper, we study the…
In this paper we make an initial study on type D moduli spaces in positive characteristic $p\neq 2$, where we allow $p$ ramified in the definite quaternion algebra. We classify the isogeny classes of $p$-divisible groups with additional…
We prove a conjecture of Milne pertaining to the existence of integral canonical models of Shimura varieties of abelian type in arbitrary unramified mixed characteristic $(0,p)$. As an application we prove for $p=2$ a motivic conjecture of…
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…