Greenberg's functional equation conjecture for ordinary Selmer groups

Let $V$ be a finite-dimensional $\d835\dd34_p$-vector space with a continuous $\d835\dd34\d835\dd34\d835\dd34\d835\dd34\d835\dd34(\d835\dd34\dd34\d835\dd34\d835\dd34\d835\dd34/\d835\dd34_p)$-action, and let $T$ be a stable $\d835\dd34_p$-lattice in $V$, with $A=V/T$. Let $\d835\dd34_\d835\dd34_\d835\dd34$ be the cyclotomic $\d835\dd34_p$-extension of $\d835\dd34$, with Galois group $\d835\dd34$, and let $S_A(\d835\dd34_\d835\dd34_\d835\dd34)$ denote the Greenberg Selmer group. Write $\d835\dd34=\d835\dd34_p\llbracket \d835\dd34\rrbracket$, let $\d835\dd34$ be the involution sending $\d835\dd34$ to $\d835\dd34^{-1}$, and let $M^{\iota}$ denote the resulting twist of a $\d835\dd34$-module. Set $A^*=\operatorname{Hom}(V,\d835\dd34_p(1))/\operatorname{Hom}(T,\d835\dd34_p(1))$. A module is $p$-critical when $V$ has the $p$-critical property used in Greenberg's conjecture. Greenberg's functional equation conjecture. One should expect that

$$S_A(\d835\dd34_\d835\dd34_\d835\dd34)^{\vee}\sim S_{A^*}(\d835\dd34_\d835\dd34_\d835\dd34)^{\vee,\iota}$$

when $V$ is $p$-critical. This refines the equality of characteristic ideals predicted by the algebraic functional equation and concerns the Selmer modules themselves; the supplied text does not state whether the conjecture has been resolved.