Coates–Sujatha fine Selmer group conjecture

Let $F$ be a number field, let $p$ be an odd prime, and let $F_\text{cyc}$ be the cyclotomic $\mathbb{Z}_p$-extension of $F$. For an elliptic curve $E$ over $F$, write $R(E/F_\text{cyc})$ for its fine Selmer group and $R(E/F_\text{cyc})^\vee$ for its Pontryagin dual. Coates–Sujatha conjecture. For all elliptic curves $E$ over $F$, the module $R(E/F_\text{cyc})^\vee$ is finitely generated over $\mathbb{Z}_p$.

This conjecture connects the structure of fine Selmer groups with Iwasawa's $\mu=0$ conjecture. The source presents it as a conjecture of Coates and Sujatha; its resolution status is not specified in the supplied text.