Every finite abelian group is the group of rational points of an ordinary abelian variety over $\mathbb{F}_2$
Stefano Marseglia, Caleb Springer · 2021
We show that every finite abelian group $G$ occurs as the group of rational points of an ordinary abelian variety over $\mathbb{F}_2$. We produce partial results for abelian varieties over a general finite field $\mathbb{F}_q$. In particular, we show that certain abelian groups cannot occur as groups of rational points of abelian varieties over $\mathbb{F}_q$ when $q$ is large.