Every positive integer is the order of an ordinary abelian variety over ${\mathbb F}_2$
Number Theory
2021-06-30 v3 Algebraic Geometry
Abstract
We show that for every integer , there is an ordinary abelian variety over that has exactly rational points.
Cite
@article{arxiv.2103.16530,
title = {Every positive integer is the order of an ordinary abelian variety over ${\mathbb F}_2$},
author = {Everett W. Howe and Kiran S. Kedlaya},
journal= {arXiv preprint arXiv:2103.16530},
year = {2021}
}
Comments
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