Torsion of elliptic curves over $\mathbb{Q}_p$ with good reduction in cyclotomic extensions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910101885943808 |
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| author | Ozeki, Yoshiyasu Yoshida, Manabu |
| author_facet | Ozeki, Yoshiyasu Yoshida, Manabu |
| contents | In this paper, for every prime $p$ and every $0\le n\le \infty$, we classify the structure of the torsion subgroup of the group of $\mathbb{Q}_p(μ_{p^n})$-rational points of elliptic curves over $\mathbb{Q}_p$ with good reduction, where $μ_{p^n}$ is the set of the $p^n$-th roots of unity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13172 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Torsion of elliptic curves over $\mathbb{Q}_p$ with good reduction in cyclotomic extensions Ozeki, Yoshiyasu Yoshida, Manabu Number Theory 11G07, 14G20 In this paper, for every prime $p$ and every $0\le n\le \infty$, we classify the structure of the torsion subgroup of the group of $\mathbb{Q}_p(μ_{p^n})$-rational points of elliptic curves over $\mathbb{Q}_p$ with good reduction, where $μ_{p^n}$ is the set of the $p^n$-th roots of unity. |
| title | Torsion of elliptic curves over $\mathbb{Q}_p$ with good reduction in cyclotomic extensions |
| topic | Number Theory 11G07, 14G20 |
| url | https://arxiv.org/abs/2510.13172 |