Integral canonical models of Shimura varieties of preabelian type

Vasiu, Adrian

doi:10.4310/ajm.1999.v3.n2.a8

Cited by 71 publications

(220 citation statements)

References 65 publications

Supporting

Mentioning

216

Contrasting

Order By: Relevance

“…Let (M, F 1 , φ, ψ) be the principally quasi-polarized filtered Dieudonné module over k of z * ((D d,1,l , Λ D d,1,l ) N ). Let G 1B(k) be the connected subgroup of GL GL GL M [ 1 p ] that corresponds naturally to G via Fontaine comparison theory, as in [Va1,Subsubsects. 5.3.4 and 5.6.5].…”

Section: ])mentioning

confidence: 99%

“…It is easy to see that the axioms 4.1 (i) and (ii) hold for the triple (M, φ, G) and that e − = dim(X) = dim(M) (to be compared with [Va1,Subsubsects. 5.4.6 and 5.4.7]).…”

Section: ])mentioning

confidence: 99%

“…Based on this and the property (iii), we get that G is smooth over Spec(W (k)). One can use Faltings deformation theory as in [Va1,Subsect. 5.4], to check that M is a quasi Shimura p-variety of Hodge type relative to F := {(M, gφ, ψ, G)|g ∈ G(W (k))} and that, up to natural identifications, F does not depend on the choice of the point y ∈ M(k).…”

Section: ])mentioning

confidence: 99%

See 2 more Smart Citations

Level 𝑚 stratifications of versal deformations of 𝑝-divisible groups

Vasiu

2008

J. Algebraic Geom.

Self Cite

View full text Add to dashboard Cite

show abstract

Section: ])mentioning

confidence: 99%

“…It is easy to see that the axioms 4.1 (i) and (ii) hold for the triple (M, φ, G) and that e − = dim(X) = dim(M) (to be compared with [Va1,Subsubsects. 5.4.6 and 5.4.7]).…”

Section: ])mentioning

confidence: 99%

Section: ])mentioning

confidence: 99%

See 1 more Smart Citation

Level 𝑚 stratifications of versal deformations of 𝑝-divisible groups

Vasiu

2008

J. Algebraic Geom.

Self Cite

View full text Add to dashboard Cite

show abstract

“…is only a variant of Zariski Main Theorem). In [Va1,3.1.2.1 c)] we overlooked the phenomenon of exceptional nilpotent such ideals and so the extra hypothesis of 1.1 (d) for p = 2 does not show up in [Va1,3.1.2.1 c)]. Theorem 1.1 (resp.…”

Section: ] (The Definition Is Recalled In 232)mentioning

confidence: 99%

On two theorems for flat, affine group schemes over a discrete valuation ring

Vasiu

2005

Open Mathematics

Self Cite

View full text Add to dashboard Cite

ABSTRACT. We include short and elementary proofs of two theorems that characterize reductive group schemes over a discrete valuation ring, in a slightly more general context. MSC 2000: Primary 11G10, 11G18, 14F30, 14G35, 14G40, 14K10, and 14J10. \ KEY WORDS: Group schemes and discrete valuation rings. §1. IntroductionLet k be a field. Let p ∈ {0} ∪ {n ∈ N|n is a prime} be the characteristic of k. Let V be a discrete valuation ring of residue field k. Let π be a uniformizer of V and let] be the field of fractions of V . Let F = Spec(P ) and G = Spec(R) be flat, affine group schemes over V . We will assume that F is a reductive group scheme over V ; so F is smooth over V and its fibres are connected and reductive groups over fields. In this paper we present elementary and short proofs of the following two basic theorems on reductive group schemes over V . (b) If p = 2, we assume that the group GK has no normal subgroup that is isomorphic to SO 2n+1 for some n ∈ N. Then G is a reductive group scheme over V .(c) The normalization G n of G is a finite G-scheme. Moreover, there is a faithfully flat V -algebraṼ that is a discrete valuation ring and such that the normalization (GṼ ) n of GṼ is a reductive group scheme overṼ .

show abstract

“…5.16), and it is a moduli scheme. The hodge case 85 was proved by Vasiu (1999) except for a small set of primes. In this case, S p (G, X ) is the normalization of the zariski closure of Sh p (G, X ) in S p (G( ), X( )).…”

Section: The Good Reduction Of Shimura Varietiesmentioning

confidence: 96%