Anticyclotomic fine Selmer cofiniteness conjecture

Let $l$ be an odd prime, let $F$ be an imaginary quadratic field, and let $\mathcal{E}$ be an elliptic curve over $F$. Let $F^{\mathrm{anti}}$ be the anticyclotomic $\mathbb{Z}_l$-extension of $F$, and let $R_{l^{\infty}}(\mathcal{E}/F^{\mathrm{anti}})$ be the fine $l^{\infty}$-Selmer group. The anticyclotomic fine Selmer conjecture. The group $R_{l^{\infty}}(\mathcal{E}/F^{\mathrm{anti}})$ is a cofinitely generated $\mathbb{Z}_l$-module. The paper proposes this as the anticyclotomic counterpart of the Coates–Sujatha conjecture and proves an equivalence with the Heegner-point conjecture A in a specified supersingular split-prime setting.