# 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}
}```
• 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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