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

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.