Every positive integer is the order of an ordinary abelian variety over ${\mathbb{F}}_2$

Abstract

We show that for every integer $m>0$, there is an ordinary abelian variety over ${\mathbb{F}}_2$ that has exactly $m$ rational points.

6 pages. Edited introduction. Changed statement of main theorem to include the observation (due to Marseglia and Springer) that our construction produces squarefree varieties. Included discussion of followup work by other groups of authors