Coates–Fukaya–Kato–Sujatha–Venjakob $M_H(G)$-conjecture for signed Selmer groups

Let $F_{\infty}/F$ be the extension in the paper, let $G=\operatorname{Gal}(F_{\infty}/F)$, and let $H$ be the subgroup specified by the extension, with completed group ring $\mathbb{Z}_p[[H]]$. For each choice of signs ${\vec{s}}$, let $X^{\vec{s}}(E/F_{\infty})$ be the Pontryagin dual of the corresponding signed Selmer group, and let $X^{\vec{s}}(E/F_{\infty})[p^{\infty}]$ denote its $p$-power torsion submodule. $\mathfrak{M}_H(G)$-conjecture. For all choices of ${\vec{s}}$, the module

$$X^{\vec{s}}(E/F_{\infty})/X^{\vec{s}}(E/F_{\infty})[p^{\infty}]$$

is finitely generated over $\mathbb{Z}_p[[H]]$. The source presents this as an extension of the $\mathfrak{M}_H(G)$-conjecture to signed Selmer groups and states that it is not used in the subsequent calculations; no resolution is given.