The virtual cohomological dimension conjecture for homological subgroups of the mapping class group

Let $S_g$ be a closed oriented surface of genus $g$, let $\Mod(S_g)$ be its mapping class group, and let $\I^k(S_g)$ be the subgroup consisting of elements that act trivially on a fixed $2k$-dimensional symplectic subspace of $H_1(S_g,\mathbb{Z})$. The virtual cohomological dimension conjecture. For $g \geq 2$ and $0 \leq k \leq g$,

$$\vcd(\I^k(S_g)) = 4g-5-k.$$

This extends the known formula $\vcd(\Mod(S_g))=4g-5$ and predicts the virtual cohomological dimensions of the intermediate subgroups $\I^k(S_g)$. The source presents the statement as a conjecture and gives a lower-bound construction, but does not state a resolution.