Mazur–Swinnerton-Dyer's Iwasawa main conjecture for elliptic curves

Choose a topological generator $\gamma\in\Gamma$, and fix an isomorphism $\Lambda\cong\mathbb{Z}_{p}[[T]]$ via $\gamma\mapsto 1+T$. Let $K/\mathbb{Q}$ be an abelian extension, let $E_{\mathbb{Q}}$ be an elliptic curve, and let $E$ denote its scalar extension to $K$. Assume that $K\cap\mathbb{Q}_{\infty}=\mathbb{Q}$ in a fixed algebraic closure $\overline{\mathbb{Q}}$, and suppose that $E$ has good ordinary reduction at all primes of $K$ lying over $p$.

Mazur–Swinnerton-Dyer's conjecture. There is an equality of ideals in $\Lambda$

$$\operatorname{Char}_{\Lambda}({\rm Sel}_{E}(K_{\infty})[p^{\infty}]^{\lor})=(L_{p}(E,T)),$$

where $L_{p}(E,T)$ is the $p$-adic $L$-function of $E/K$.

This is the elliptic-curve analogue of the Iwasawa main conjecture, relating the characteristic ideal of the Selmer-group dual to a $p$-adic $L$-function. The supplied source gives no resolution status for this formulation.