English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We describe a probability distribution on isomorphism classes of principallyquasi-polarized p-divisible groups over a finite field k of characteristic pwhich can reasonably be thought of as "uniform distribution," and we computethe distribution of various statistics (p-corank, a-number, etc.) ofp-divisible groups drawn from this distribution. It is then natural to ask towhat extent the p-divisible groups attached to a randomly chosen hyperellipticcurve (resp. curve, resp. abelian variety) over k are uniformly distributed inthis sense. For instance, one can ask whether the proportion of genus-g curvesover F_p whose Jacobian is ordinary approaches the limit that such a heuristicwould predict. This heuristic is analogous to conjectures of Cohen-Lenstra typefor fields k of characteristic other than p, in which case the randomp-divisible group is defined by a random matrix recording the action ofFrobenius. Extensive numerical investigation reveals some cases of agreementwith the heuristic and some interesting discrepancies. For example, planecurves over F_3 appear substantially less likely to be ordinary thanhyperelliptic curves over F_3.

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