A note on the order of the Tate--Shafarevich group modulo squares
Number Theory
2024-04-26 v1
Abstract
We investigate the order of the Tate--Shafarevich group of abelian varieties modulo rational squares. Our main result shows that every square-free natural number appears as the non square-free part of the Tate--Shafarevich group of some abelian variety, thereby validating a conjecture of W. Stein.
Keywords
Cite
@article{arxiv.2404.16785,
title = {A note on the order of the Tate--Shafarevich group modulo squares},
author = {Alexandros Konstantinou},
journal= {arXiv preprint arXiv:2404.16785},
year = {2024}
}
Comments
8 pages