Torsion groups of elliptic curves over the $\mathbb Z_p$-extensions of $\mathbb Q$

TL;DR

This paper classifies the torsion subgroups of elliptic curves over the infinite $Z_p$-extensions of $Q$, providing a comprehensive understanding of how torsion groups behave in these infinite extensions.

Contribution

It determines all possible torsion groups of elliptic curves over the $Z_p$-extensions of $Q$, extending prior classifications to infinite extensions.

Findings

Complete classification of torsion groups over $Z_p$-extensions

Identification of all possible torsion subgroup structures

Extension of known results to infinite Galois extensions

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 $\mathbb Q$.