Level 𝑚 stratifications of versal deformations of 𝑝-divisible groups

Vasiu, Adrian

doi:10.1090/s1056-3911-08-00495-5

Cited by 15 publications

(71 citation statements)

References 28 publications

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“…7,Rm. iii), p. 136]). If G is smooth over W (k), then the reduced formal scheme C k (G, B G ) red of C k (G, B G ) is formally smooth (the proof of this is the same as of [Va3,Cor. If G is smooth over W (k), then the reduced formal scheme C k (G, B G ) red of C k (G, B G ) is formally smooth (the proof of this is the same as of [Va3,Cor.…”

Section: Local Traverso Stratamentioning

confidence: 93%

“…We recall that s D is a stratum of the Traverso stratification of A k (or of A itself) introduced in [Va2,Thm. also [Va3,Subsubsect. 5.3.2] (cf.…”

Section: 3])mentioning

confidence: 99%

“…Strictly speaking, Traverso used a codimension in a certain orbit space context (see [Tr,Thm. Recently, the Traverso formula was proved in [Oo] and [Va3,Thm. We call Formula (21) (or its codimension form) as Traverso's formula.…”

Section: 3])mentioning

confidence: 99%

“…4], etc.) 5.3.2] or [Va3,Subsubsect. A very important stratification of S is the Traverso (ultimate) stratification which can be defined similarly to either [Va2,Thm.…”

Section: Introductionmentioning

confidence: 99%

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Deformation subspaces of $p$-divisible groups as formal Lie groups associated to $p$-divisible groups

Vasiu¹

2011

J. Algebraic Geom.

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Let k be an algebraically closed field of characteristic p > 0. Let D be a p-divisible group over k which is not isoclinic. Let D (resp. D k ) be the formal deformation space of D over Spf(W (k)) (resp. over Spf(k)). We use axioms to construct formal subschemes G k of D k that: (i) have canonical structures of formal Lie groups over Spf(k) associated to pdivisible groups over k, and (ii) give birth, via all geometric points Spf(K) → G k , to p-divisible groups over K that are isomorphic to D K . We also identify when there exist formal subschemes G of D which lift G k and which have natural structures of formal Lie groups over Spf(W (k)) associated to p-divisible groups over W (k). Applications to Traverso (ultimate) stratifications are included as well.

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Section: Local Traverso Stratamentioning

confidence: 93%

“…We recall that s D is a stratum of the Traverso stratification of A k (or of A itself) introduced in [Va2,Thm. also [Va3,Subsubsect. 5.3.2] (cf.…”

Section: 3])mentioning

confidence: 99%

Section: 3])mentioning

confidence: 99%

“…4], etc.) 5.3.2] or [Va3,Subsubsect. A very important stratification of S is the Traverso (ultimate) stratification which can be defined similarly to either [Va2,Thm.…”

Section: Introductionmentioning

confidence: 99%

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Deformation subspaces of $p$-divisible groups as formal Lie groups associated to $p$-divisible groups

Vasiu¹

2011

J. Algebraic Geom.

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“…The Shimura datum (G, X) determine a cocharacter µ : G m,W (κ) → G Zp ⊗ W (κ) which is unique up to G Zp (W (κ))-conjugacy. We introduce in this subsection some group theoretic settings which are essentially from [39] section 4. For simplicity, we write G R for…”

Section: 3mentioning

confidence: 99%

Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type

Zhang¹

2018

Can. j. math.

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Abstract. For a Shimura variety of Hodge type with hyperspecial level structure at a prime p, Vasiu and Kisin constructed a smooth integral model (namely the integral canonical model) uniquely determined by a certain extension property. We de ne and study the Ekedahl-Oort strati cations on the special bers of those integral canonical models when p > . is generalizes Ekedahl-Oort strati cations de ned and studied by Oort on moduli spaces of principally polarized abelian varieties and those de ned and studied by Moonen, Wedhorn and Viehmann on good reductions of Shimura varieties of PEL type. We show that the Ekedahl-Oort strata are parameterized by certain elements w in the Weyl group of the reductive group in the Shimura datum. We prove that the stratum corresponding to w is smooth of dimension l(w) (i.e. the length of w) if it is non-empty. We also determine the closure of each stratum.

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Mod p classification of Shimura F ‐crystals

Vasiu¹

2010

Mathematische Nachrichten

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Let k be an algebraically closed field of positive characteristic p. We first classify the D-truncations mod p of Shimura F -crystals over k and then we study stratifications defined by inner isomorphism classes of these D-truncations. This generalizes previous works of Kraft, Ekedahl, Oort, Moonen, and Wedhorn. As a main tool we introduce and study Bruhat F -decompositions; they generalize the combined form of Steinberg theorem and of classical Bruhat decompositions for reductive groups over k.

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Level 𝑚 stratifications of versal deformations of 𝑝-divisible groups

Cited by 15 publications

References 28 publications

Deformation subspaces of $p$-divisible groups as formal Lie groups associated to $p$-divisible groups

Deformation subspaces of $p$-divisible groups as formal Lie groups associated to $p$-divisible groups

Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type

Mod p classification of Shimura F ‐crystals

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