Super-Isolated Abelian Varieties
Number Theory
2019-02-13 v2
Abstract
We call an abelian variety over a finite field super-isolated if its (-rational) isogeny class contains a single isomorphism class. In this paper, we use the Honda-Tate theorem to characterize super-isolated ordinary simple abelian varieties by certain algebraic integers. Our main result is that for a fixed dimension , there are finitely many such varieties.
Cite
@article{arxiv.1809.03649,
title = {Super-Isolated Abelian Varieties},
author = {Travis Scholl},
journal= {arXiv preprint arXiv:1809.03649},
year = {2019}
}
Comments
Fixed various typos, added additional motivation to the introduction, and rewrote parts of section 5 to be more clear