Integral Canonical Models of Shimura Varieties of Preabelian Type

By A. Vasiu. 2003

113 citations recorded by the source corpus.

We prove the existence of integral canonical models of Shimura varieties of preabelian type with respect to primes of characteristic at least 5.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/21eb3802396ca670da6aecc48d353481f2be7757

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type (2013, methodology): “Integral canonical models are constructed by Vasiu in [22] and Kisin in [7].”
Integral canonical models for Spin Shimura varieties (2012, background): “der the pro-scheme: SKp = lim←− K′⊂K SK′. Here, K′ varies over compact open sub-groups of Kwith K′ p = Kp. We have the following result, due (independently) to Kisin [Kis10, 2.3.8, 3.4.14], and Vasiu [Vas99]. Theorem 4.4. SKp is a smooth integral canonical model for ShKp over Z(p). Moreover, the ﬁni”
Some Cases of the Mumford-Tate Conjecture and Shimura Varieties (2002, methodology): “sp. (Hab,Xab)), cf. [Va1, Subsubsection 2.4.1]. We say (H,X) (or Sh(H,X)) is unitary if the group Had is non-trivial and each simple factor of Had Q is of some An Lie type. 3 1.2.1. On techniques. In [Va1] we developed some techniques to study Shimura varieties and local deformations of abelian vari”
The \mu-ordinary locus for Shimura varieties of Hodge type (2013, background): “tale component of the absolute Hodge cycle (sdR,ξ,(set,l,ξ´ )) to its de Rham component. If Aξ can be deﬁned over a number ﬁeld, this is a theorem of Blasius and Wintenberger ([Bl], 0.3.), and Vasiu ([Va1], 5.2.16.) observed that their result can also be extended to our more general situation. (iii)”
Strata Hasse invariants, Hecke algebras and Galois representations (2015, methodology): “duces the general framwork of PEL-type Shimura varieties and constructs models at primes of good reduction. This construction was then generalized by Kisin-Vasiu to the Hodge-type case in [Kis10] and [Vas99]. The special ﬁber of the Shimura variety is then a smooth quasi-projective scheme over a ﬁni”
Crystalline Boundedness Principle (2002, background): “The paper [40] and many previous ones (like [25]) deal with particular cases of such triples (M, ϕ, G)'s: the pair (M, ϕ) is a Dieudonné module over k, the group scheme G is reductive, and there exists a semisimple element s ϕ ∈ G(B(k)) whose eigenvalues are 1 and p and such that ϕs −1 ϕ is a…”