Visible 2-torsion in the Tate-Shafarevich group of an elliptic curve
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914618227556352 |
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| author | Fisher, Tom |
| author_facet | Fisher, Tom |
| contents | We show that every pair of 2-torsion elements in the Tate-Shafarevich group of an elliptic curve are visible in the same abelian surface. This was previously only known for a single 2-torsion element. Our result explains some of the original observations on visibility in the paper of Cremona and Mazur. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31488 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Visible 2-torsion in the Tate-Shafarevich group of an elliptic curve Fisher, Tom Number Theory 11G05, 14G12 We show that every pair of 2-torsion elements in the Tate-Shafarevich group of an elliptic curve are visible in the same abelian surface. This was previously only known for a single 2-torsion element. Our result explains some of the original observations on visibility in the paper of Cremona and Mazur. |
| title | Visible 2-torsion in the Tate-Shafarevich group of an elliptic curve |
| topic | Number Theory 11G05, 14G12 |
| url | https://arxiv.org/abs/2605.31488 |