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.
Categories: math.NT