Coates–Fukaya–Kato–Sujatha–Venjakob finiteness conjecture

Let $K$ be a number field, let $p$ be a prime, let $E$ be an elliptic curve over $K$, and let $L/K$ be a Galois extension with $G=\operatorname{Gal}(L/K)$ containing a closed normal subgroup $H$ such that $G/H\cong {\mathbb Z}_p$. Write $\operatorname{\Lambda}(G)={\mathbb Z}_p[[G]]$, let $X(E/L)$ be the Pontryagin dual of the Selmer group, and let $X(E/L)(p)$ be its maximal $p$-power-torsion submodule. Coates–Fukaya–Kato–Sujatha–Venjakob conjecture. If $E$ has ordinary reduction at every prime of $K$ over $p$, then $X(E/L)/X(E/L)(p)$ is a finitely generated $\operatorname{\Lambda}(H)$-module. This finiteness condition is the stronger hypothesis used to construct noncommutative algebraic $p$-adic $L$-functions in the cited formalism. The source states it as conjectural and gives no resolution in the stated generality.