A note on the order of the Tate--Shafarevich group modulo squares
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914770587746304 |
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| author | Konstantinou, Alexandros |
| author_facet | Konstantinou, Alexandros |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the order of the Tate--Shafarevich group modulo squares Konstantinou, Alexandros Number Theory 11G10 (Primary), 11G40 (Secondary) 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. |
| title | A note on the order of the Tate--Shafarevich group modulo squares |
| topic | Number Theory 11G10 (Primary), 11G40 (Secondary) |
| url | https://arxiv.org/abs/2404.16785 |