2013
DOI: 10.1017/s1474748012000862
|View full text |Cite
|
Sign up to set email alerts
|

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

Abstract: 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 … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

2
18
0

Year Published

2014
2014
2020
2020

Publication Types

Select...
5

Relationship

0
5

Authors

Journals

citations
Cited by 9 publications
(20 citation statements)
references
References 18 publications
2
18
0
Order By: Relevance
“…the error is bounded by D/ √ q for some constant D which depends only on g, n and p. Thanks to Lemma 2.2, this is compatible with the broad philosophy of [5], and even that of [9]; a (polarized) group (scheme) occurs with frequency inversely proportional to the size of its automorphism group.…”
Section: Introductionsupporting
confidence: 60%
See 1 more Smart Citation
“…the error is bounded by D/ √ q for some constant D which depends only on g, n and p. Thanks to Lemma 2.2, this is compatible with the broad philosophy of [5], and even that of [9]; a (polarized) group (scheme) occurs with frequency inversely proportional to the size of its automorphism group.…”
Section: Introductionsupporting
confidence: 60%
“…The present investigation was inspired by the work of Cais, Ellenberg and Zureick-Brown, even though the results here are incomparable with those of [5]. The author acknowledges helpful discussions with Oort and Liedtke, especially concerning the example in Section 5.3.…”
Section: Introductionmentioning
confidence: 90%
“…Some recent work has been done on generating data and developing a heuristic for the case where the prime p for which the p-rank is under consideration is equal to the characteristic of the field. See [7] for some new results along these lines.…”
Section: Resultsmentioning
confidence: 95%
“…if and only if D ∼ Θ geom . But the proof of Theorem 2 (or of [CEZB,Thm. 4.2]) is precisely about showing that if c i,j = 0 for some i and j that are both odd, then Θ arith ∼ Θ geom .…”
Section: Connections With the Rank Of The Hasse-witt Matrixmentioning
confidence: 99%
“…The starting point of this article is a recent theorem by Cais, Ellenberg and Zureick-Brown [CEZB,Thm. 4.2], asserting that over a finite field k of characteristic 2, almost all smooth plane projective curves of a given odd degree d ≥ 3 have a non-trivial krational 2-torsion point on their Jacobian.…”
Section: Introductionmentioning
confidence: 99%