Abstract
Let denote the number of isomorphism classes of -dimensional Abelian varieties over the finite field of size . Let denote the number of isomorphism classes of principally polarized -dimensional Abelian varieties over the finite field of size . We derive upper bounds for and lower bounds for for fixed and increasing. The extremely large gap between the lower bound for and the upper bound for implies some statistically counterintuitive behavior for Abelian varieties of large dimension over a fixed finite field.
Citation
Michael Lipnowski. Jacob Tsimerman. "How large is ?." Duke Math. J. 167 (18) 3403 - 3453, 1 December 2018. https://doi.org/10.1215/00127094-2018-0029
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