Greenberg–Ochiai's two-variable Iwasawa main conjecture for Hida deformations

Let $d53c$ be the coefficient ring of a residually reducible Hida deformation, let $d54b$ be a stable free lattice, and put

$$\mathcal{T}=\mathbb{T}\hat{\otimes}_{\mathbb{Z}_p}\mathbb{Z}_p[[\Gamma]](\tilde{\kappa}^{-1}),\qquad \mathcal{A}=\mathcal{T}\otimes_{\mathcal{R}}\mathcal{R}^{\lor}.$$

Write $\operatorname{Sel}_{\mathcal{A}}$ for the associated Selmer group and $L_p^{\mathrm{Ki}}(\mathcal{T})$ for the two-variable Mazur–Kitagawa $p$-adic $L$-function. Greenberg–Ochiai's two-variable main conjecture. Suppose that $\mathbb{I}$ is a UFD and Gorenstein, and assume (Eis) and $\chi\neq\omega$. For every stable free lattice $\mathbb{T}$,

$$\operatorname{char}_{\mathcal{R}}(\operatorname{Sel}_{\mathcal{A}})^{\lor}=\left(L_p^{\mathrm{Ki}}(\mathcal{T})\right).$$

This is the two-variable Iwasawa main conjecture for the Hida deformation; it relates the characteristic ideal of the Pontryagin dual Selmer group to the analytic $p$-adic $L$-function. The supplied text gives no resolution.