Related papers: Integral canonical models of unitary Shimura varie…
We prove the existence of integral canonical models of Shimura varieties of preabelian type with respect to primes of characteristic at least 5.
We prove that Shimura varieties admit integral canonical models for sufficiently large primes. In the case of abelian-type Shimura varieties, this recovers work of Kisin-Kottwitz for sufficiently large primes. We also prove the existence of…
We construct relative PEL type embeddings in mixed characteristic (0,2) between hermitian orthogonal Shimura varieties of PEL type. We use this to prove the existence of integral canonical models in unramified mixed characteristic (0,2) of…
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 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…
We prove the existence of weak integral canonical models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic $(0,p)$. As a first application we solve a conjecture of Langlands for Shimura varieties of Hodge type.…
Let $(G,X)$ be a Shimura variety of PEL type such that $G_{{\bf Q}_2}$ is a split ${\bf GSO}_{2n}$ group with $n\ge 2$. We prove the existence of the integral canonical models of ${\rm Sh}(G,X)/H_2$ in unramified mixed characteristic…
We define and construct integral canonical models for automorphic vector bundles over Shimura varieties of abelian type. More precisely, we first build on Kisin's work to construct integral canonical models over rings of integers of number…
We show how to characterize integral models of Shimura varieties over places of the reflex field where the level subgroup is parahoric by formulating a definition of a "canonical" integral model. We then prove that in Hodge type cases and…
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…
This is a survey of the three main methods developed in the last 15 years to prove the existence of integral canonical models of Shimura varieties of Hodge type. The only new part is formed by corrections to results of Kisin.
We prove a conjecture of Pappas and Rapoport for all Shimura varieties of abelian type with parahoric level structure when $p>3$ by showing that the Kisin-Pappas-Zhou integral models of Shimura varieties of abelian type are canonical. In…
We construct regular integral canonical models for Shimura varieties attached to Spin groups at (possibly ramified) odd primes. We exhibit these models as schemes of 'relative PEL type' over integral canonical models of larger Spin Shimura…
We compute the arithmetic volumes of integral models of unitary Shimura curves. This establishes the base case of an inductive argument to compute the arithmetic volumes of unitary Shimura varieties of higher dimension, to appear in…
In this paper we recall the construction and basic properties of complex Shimura varieties and show that these properties actually characterize them. This characterization immediately implies the explicit form of Kazhdan's theorem on the…
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…
The Kodaira dimension of Shimura varieties has been studied by many people. Kondo and Gritsenko-Hulek-Sankaran studied the singularities of orthogonal Shimura varieties related to the moduli spaces of polarized K3 surfaces. They proved that…
In this paper we generalize Cherednik's method and prove that certain Shimura varieties corresponding to groups of unitary similitudes and automorphic vector bundles over them have p-adic uniformization. This is proved for Shimura…
We prove in this paper a classicality result for overconvergent modular forms on PEL Shimura varieties of type (A) or (C), without any ramification hypothesis. We use an analytic continuation method, which generalizes previous results in…
In this article, we study admissible representations of even unitary groups over local fields, where the quadratic extension is ramified, with invariant vectors under the action of the stabilizer of a unimodular lattice and some properties…