On the Fine Selmer Group

Abstract

Let $E/\mathbb{Q}$ be an elliptic curve, $p$ an odd prime and $K_{\infty }/K$ the anticyclotomic ${\mathbb{Z}}_p$-extension of a quadratic imaginary field $K$. In a previous article the author conjectured that the fine $p^{\infty }$-Selmer group $R_{p^{\infty }}(E/K_{\infty })$ is confinitely generated over ${\mathbb{Z}}_p$. In this note we prove this conjecture assuming some hypotheses on $E$ and $p$.

This paper has been withdrawn due to an error in the proof