Greenberg's vanishing conjecture for the second cohomology group

Let $F$ be a number field, let $F_{\infty}$ be its cyclotomic $\mathbf{Z}_{p}$-extension, let $V$ be a critical nearly ordinary Galois representation, and let $A=V/T$ be a torsion quotient for a $G_F$-stable lattice $T$. Let $\Sigma$ be a finite set of places sufficiently large for $A$, and write $F_{\Sigma}$ for the maximal extension of $F$ unramified outside $\Sigma$. Greenberg's conjecture.

$$H^{2}(F_{\Sigma}/F_{\infty},A)=0.$$

The vanishing removes the error term in the lower bound for the $\Lambda$-corank of the critical Selmer group, where $\Lambda=\mathcal{O}[[\operatorname{Gal}(F_{\infty}/F)]]$. The source attributes this conjecture to Greenberg; its resolution is not specified here.