Greenberg–Mazur Iwasawa main conjecture for elliptic curves

Let $p$ be an odd prime and $E$ an elliptic curve with good ordinary reduction at $p$. Let $

$$\Lambda=\mathbb{Z}_p\llbracket \mathrm{Gal}(\mathbb{Q}_\infty/\mathbb{Q})\rrbracket\simeq\mathbb{Z}_p\llbracket T\rrbracket$$

be the cyclotomic Iwasawa algebra, and let $L_p(E)\in\Lambda$ be the $p$-adic $L$-function. For a $$\Lambda$-module$M$, write$M^\vee$for its Pontryagin dual and$\operatorname{char}{\Lambda}(M)$for its characteristic ideal. **Iwasawa main conjecture.** The Selmer group$\mathrm{Sel}(\mathbb{Q}\infty,E[p^\infty])$is$\Lambda$-cotorsion, and

$$\left(L_p(E)\right)=\operatorname{char}_{\Lambda}\left(\mathrm{Sel}(\mathbb{Q}_\infty,E[p^\infty])^\vee\right)$$

as ideals of $\Lambda$. This is the cyclotomic Iwasawa-theoretic relation between the $p$-adic $L$-function and the Selmer group, and is presented here as the elliptic-curve analogue of the classical Iwasawa main conjecture. The supplied text gives no resolution status for this formulation.