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.

26 pages, some minor revisions, including a rewrite of the opening of the Introduction