每个正整数都是 ${\mathbb F}_2$ 上普通阿贝尔簇的阶
数论
2021-06-30 v3 代数几何
摘要
我们证明对任意整数 ，存在一个定义在 上的普通阿贝尔簇，它恰好有 个有理点。
引用
@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}
}
备注
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