On the Lambda-cotorsion subgroup of the Selmer group (1812.00207v3)

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.