Fine Selmer torsion conjecture for elliptic modular forms

Let $f$ be a normalized cuspidal eigenform as in the source, let $A_f$ be the associated discrete Galois representation, and let $F_\infty$ be a $\mathbb{Z}_{p}$-extension of a number field $F$. Write $\Gamma=\operatorname{Gal}(F_\infty/F)$ and let $Y(A_f/F_\infty)$ be the Pontryagin dual of the fine Selmer group. Fine Selmer torsion conjecture for modular forms. The module $Y(A_f/F_\infty)$ is torsion over

$$\mathcal{O}[[\Gamma]],$$

where $\mathcal{O}$ is the coefficient ring attached to $f$. This is the natural modular-form analogue of the fine Selmer torsion conjecture for abelian varieties. The paper develops evidence in ordinary Hida-family settings, but the assertion is not proved in general.