English

Super-Isolated Abelian Varieties

Number Theory 2019-02-13 v2

Abstract

We call an abelian variety over a finite field Fq\mathbb{F}_q super-isolated if its (Fq\mathbb{F}_q-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 g3g \geq 3, there are finitely many such varieties.

Keywords

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

R2 v1 2026-06-23T04:01:45.185Z