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arXiv · 2510.13172

Torsion of elliptic curves over $\mathbb{Q}_p$ with good reduction in cyclotomic extensions

Yoshiyasu Ozeki·Manabu Yoshida
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Abstract

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 $\mathbb{Q}_p(\mu_{p^n})$-rational points of elliptic curves over $\mathbb{Q}_p$ with good reduction, where $\mu_{p^n}$ is the set of the $p^n$-th roots of unity.

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Yoshiyasu Ozeki, Manabu Yoshida. 2025-10-15. Torsion of elliptic curves over $\mathbb{Q}_p$ with good reduction in cyclotomic extensions. https://arxiv.org/abs/2510.13172

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