How large is $A_{g}(\mathbb{F}_{q})$?

@article{Lipnowski2018HowLI,
  title={How large is \$A_\{g\}(\mathbb\{F\}_\{q\})\$?},
  author={Michael Lipnowski and Jacob Tsimerman},
  journal={Duke Mathematical Journal},
  year={2018},
  volume={167},
  pages={3403-3453}
}
  • Michael Lipnowski, Jacob Tsimerman
  • Published 2018
  • Mathematics
  • Duke Mathematical Journal
  • Let $B(g,p)$ denote the number of isomorphism classes of $g$-dimensional abelian varieties over the finite field of size $p.$ Let $A(g,p)$ denote the number of isomorphism classes of principally polarized $g$ dimensional abelian varieties over the finite field of size $p.$ We derive upper bounds for $B(g,p)$ and lower bounds for $A(g,p)$ for $p$ fixed and $g$ increasing. The extremely large gap between the lower bound for $A(g,p)$ and the upper bound $B(g,p)$ implies some statistically… CONTINUE READING
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