Torsion groups of elliptic curves over the ${\mathbb{Z}}_p$-extensions of $\mathbb{Q}$

Abstract

We determine, for an elliptic curve $E/\mathbb{Q}$ and for all $p$, all the possible torsion groups $E({\mathbb{Q}}_{\infty ,p}{)}_{tors}$, where ${\mathbb{Q}}_{\infty ,p}$ is the ${\mathbb{Z}}_p$-extension of $\mathbb{Q}$.

20 pages