Polynesian Journal of Mathematics

Volume 4, Issue 1
Special volume AJAX in honor of René Schoof

Abelian varieties over 𝔽₂ of prescribed order and dimension

Kiran S. Kedlaya

Abstract:

In a previous paper, we showed that for any fixed positive integer $m$, there exist infinitely many isogeny classes of simple abelian varieties over ${𝔽}_2$ whose group of rational points has order $m$. Here we show that for $m$ even or an odd prime or prime power, for every sufficiently large (depending on $m$) positive integer $g$, there is a simple abelian variety of dimension $g$ over ${𝔽}_2$ whose group of rational points has order $m$. This uses a result on recurrent sequences of interlaced polynomials which is presented independently in an appendix.

Citation:

Kiran S. Kedlaya. Abelian varieties over 𝔽₂ of prescribed order and dimension. Polynesian Journal of Mathematics, Volume 4, Issue 1, Pages 1–33. (Sept. 2026) DOI: 10.69763/polyjmath.4.1

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Milestones:

Received 5 Oct 2025
Revised 5 Mar 2026
Accepted 9 Mar 2026
Published 28 Sep 2026
Communicated by Samuele Anni

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