Groups of points on abelian threefolds over finite fields

Abstract

In this paper we provide an algorithm to classify groups of points on abelian threefolds over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given ${\mathbb{F}}_q$-isogeny class. This work completes partial classification given by S.Rybakov.

Cited by in corpus (2)

• Every finite abelian group is the group of rational points of an ordinary abelian variety over ${\mathbb{F}}_2$, ${\mathbb{F}}_3$ and ${\mathbb{F}}_5$
• Abelian varieties over finite fields and their groups of rational points