If R(E/Q_\infty)$R(E/\Bbb Q_{\infty})$ is the fine Selmer group and Y(E/Q_\infty)$Y(E/\Bbb Q_{\infty})$ is its dual, then we know that Y(E/Q_\infty)$Y(E/\Bbb Q_{\infty})$ is a finitely generated \Lambda$\Lambda$-module and by a theorem of Kato, it is also torsion. My understanding is that it should thus make sense to want to attach a p$p$-adic L function-function.
Can we say what this p$p$-adic L function-function is? Or does it just follow (trivially) from the Iwasawa main conjecture?