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

@article{Cais2013RandomDM,
  title={Random Dieudonn{\'e} modules, random \$p\$-divisible groups, and random curves over finite fields},
  author={Bryden R. Cais and Jordan S. Ellenberg and David Zureick-Brown},
  journal={Journal of the Institute of Mathematics of Jussieu},
  year={2013},
  volume={12},
  pages={651 - 676}
}
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… Expand
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