A Stratification of a Moduli Space of Abelian Varieties

Oort, Frans

doi:10.1007/978-3-0348-8303-0_13

Cited by 104 publications

(167 citation statements)

References 29 publications

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“…The smoothness claimed in Part (4) can be extracted from Oort's paper [29]. It was shown in a different way by Wedhorn in [32]; see Corollary 3.5 and Theorem 6.4 (at least if p > 2).…”

Section: Proposition 23mentioning

confidence: 90%

“…For (1), see [23], Theorem 4.7. Part (2), as well as the dimension formula in (3), is proved in [29], Theorem 1.2. For the equidimensionality in (3), see [24], Corollary 3.1.6.…”

Section: Proposition 23mentioning

confidence: 92%

“…Let us briefly discuss how they are related. In [29], Oort classifies EO strata by elementary sequences, i. e. maps ϕ : {0, . .…”

Section: 4mentioning

confidence: 99%

“…There is a unique one-dimensional EO stratum. See [29], §1. (1) The EO stratification is a refinement of the p-rank stratification.…”

Section: Proposition 23mentioning

confidence: 99%

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The supersingular locus in Siegel modular varieties with Iwahori level structure

Görtz

2011

Math. Ann.

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Abstract. We study moduli spaces of abelian varieties in positive characteristic, more specifically the moduli space of principally polarized abelian varieties on the one hand, and the analogous space with Iwahori type level structure, on the other hand. We investigate the Ekedahl-Oort stratification on the former, the Kottwitz-Rapoport stratification on the latter, and their relationship. In this way, we obtain structural results about the supersingular locus in the case of Iwahori level structure, for instance a formula for its dimension in case g is even.

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“…The smoothness claimed in Part (4) can be extracted from Oort's paper [29]. It was shown in a different way by Wedhorn in [32]; see Corollary 3.5 and Theorem 6.4 (at least if p > 2).…”

Section: Proposition 23mentioning

confidence: 90%

“…For (1), see [23], Theorem 4.7. Part (2), as well as the dimension formula in (3), is proved in [29], Theorem 1.2. For the equidimensionality in (3), see [24], Corollary 3.1.6.…”

Section: Proposition 23mentioning

confidence: 92%

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The supersingular locus in Siegel modular varieties with Iwahori level structure

Görtz

2011

Math. Ann.

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“…In this section let k denote an algebraically closed field of characteristic p. We recall the classification of (polarized) F -zips over k. Originally the classification of BT 1 's is due to Kraft [16], and that of polarized BT 1 's is due to Oort [23]. Now Moonen [20] and Moonen-Wedhorn [21] gave a more conceptual reinterpretation and a generalization by using Weyl groups.…”

Section: Classifying Data Of F -Zipsmentioning

confidence: 99%

Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture

Harashita¹

2010

Ann. inst. Fourier

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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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A Stratification of a Moduli Space of Abelian Varieties

Cited by 104 publications

References 29 publications

The supersingular locus in Siegel modular varieties with Iwahori level structure

The supersingular locus in Siegel modular varieties with Iwahori level structure

Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture

Mod p classification of Shimura F ‐crystals

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