Coates–Sujatha's fine Selmer conjecture

Let $E$ be an elliptic curve over a number field $F$, let $p$ be a prime at which $E$ has good reduction, and let $F_\infty$ be the cyclotomic $\mathbb{Z}_p$-extension of $F$. Denote by $\operatorname{Sel}_{p^\infty}^0(F_\infty,E)$ the fine Selmer group. Coates–Sujatha's conjecture. The group $\operatorname{Sel}_{p^\infty}^0(F_\infty,E)$ is cofinitely generated as a $\mathbb{Z}_p$-module. This conjecture is used as a structural input in the paper; the general assertion remains open.