Foliations in moduli spaces of abelian varieties

Oort, Frans

doi:10.1090/s0894-0347-04-00449-7

Cited by 74 publications

(54 citation statements)

References 20 publications

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“…We note that, unlike the a-number, p-rank, or the final type, the Newton polygon of a Dieudonné module D is not determined by D/pD. The question of which Newton polygons are compatible with which final types is a subject of active research [21]. Our expectation is that the probability distribution on the Newton polygon of D ll , conditional on the p-corank of D being c, should be given by the probability distribution on Newton polygons of nilpotent p-autodual matrices on Z 2c p .…”

Section: Other Statistics and Questions: Final Types And Newton Polygonsmentioning

confidence: 97%

Random Dieudonné modules, random -divisible groups, and random curves over finite fields

Cais¹,

Ellenberg²,

Zureick-Brown

2013

J. Inst. Math. Jussieu

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Link to this article: http://journals.cambridge.org/abstract_S1474748012000862How to cite this article: Bryden Cais, Jordan S. Ellenberg and David Zureick-Brown (2013). Random Dieudonné modules, random -divisible groups, and random curves over nite elds.Abstract We describe a probability distribution on isomorphism classes of principally quasi-polarized p-divisible groups over a finite field k of characteristic p which can reasonably be thought of as a 'uniform distribution', and we compute the distribution of various statistics (p-corank, a-number, etc.) of p-divisible groups drawn from this distribution. It is then natural to ask to what extent the p-divisible groups attached to a randomly chosen hyperelliptic curve (respectively, curve; respectively, abelian variety) over k are uniformly distributed in this sense. This heuristic is analogous to conjectures of Cohen-Lenstra type for char k = p, in which case the random p-divisible group is defined by a random matrix recording the action of Frobenius. Extensive numerical investigation reveals some cases of agreement with the heuristic and some interesting discrepancies. For example, plane curves over F 3 appear substantially less likely to be ordinary than hyperelliptic curves over F 3 .

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Section: Other Statistics and Questions: Final Types And Newton Polygonsmentioning

confidence: 97%

Random Dieudonné modules, random -divisible groups, and random curves over finite fields

Cais¹,

Ellenberg²,

Zureick-Brown

2013

J. Inst. Math. Jussieu

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“…Proof. When n = ∞, the existence of a scheme A g,ξ satisfying (3.1) is [23,Theorem 3.3]; there, such a scheme is called a 'central leaf'. For finite n, see, for example [27,Theorem 1.2].…”

Section: Stratifications On a Gmentioning

confidence: 99%

“…It has been understood for some time that A g,ξ is pure of codimension dim Aut(ξ) in A g [27,28]. For smoothness, we model our proof on that of [23,Theorem 3.13], which proves the smoothness in the case when n = ∞. (See also [27, § 4].)…”

Section: Stratifications On a Gmentioning

confidence: 99%

“…In § 3, we review (and, where necessary, extend) results, largely due to Oort [23] and to Chai and Oort [8], on the structure of the strata A g,ξ . It turns out that, although there are infinitely many such strata (if n 2), their topology (if n g 0) may be uniformly bounded in terms of g, n, and p.…”

Section: Introductionmentioning

confidence: 99%

“…purely inseparable, and the normalization morphism S → S factors as S → S N → S. To prove the formulation in Proposition 3.4, we may assume that S is integral. The normality of S implies that S N ∼ = S. An analysis of[23, Lemma 1.4] shows that one may realize T N → S N as a suitable iterate of the Frobenius morphism F(i) …”

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confidence: 99%

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