On the Lambda-cotorsion subgroup of the Selmer group

Abstract

Let $E$ be an elliptic curve defined over a number field $K$ with supersingular reduction at all primes of $K$ above $p$. If $K_{\infty }/K$ is a ${\mathbb{Z}}_p$-extension such that $E(K_{\infty })[p^{\infty }]$ is finite and $H^2(G_S(K_{\infty }),E[p^{\infty }])=0$, then we prove that the $\Lambda$-torsion subgroup of the Pontryagin dual of ${\text{Sel}}_{p^{\infty }}(E/K_{\infty })$ is pseudo-isomorphic to the Pontryagin dual of the fine Selmer group of $E$ over $K_{\infty }$. This is the Galois-cohomological analog of a flat-cohomological result of Wingberg.

made a slight change to the introduction