Gouvea's dimension conjecture for universal deformation rings

Assume that $G$ satisfies the finiteness condition $\Phi_p$, and let $V_{\mathbb F}$ be absolutely irreducible. Write $R_{V_{\mathbb F}}$ for the universal deformation ring, and let

$$\delta(\operatorname{ad}(V_{\mathbb F})):=h^2(G,\operatorname{ad})-h^1(G,\operatorname{ad}),$$

where $h^i(\cdots):=\dim_{\mathbb F}H^i(\cdots)$ for $i=1,2$.

Gouvea's dimension conjecture. In the presentation proposition for the universal deformation ring, equality always holds in the Krull-dimension bound; equivalently,

$$-\delta(\operatorname{ad}(V_{\mathbb F}))=\operatorname{Krulldim}(R_{V_{\mathbb F}}/(p)).$$

The source attributes this conjecture to Gouvea. It concerns the dimension of deformation spaces and the source gives no resolution status.