Church–Farb–Putman conjecture on codimension cohomology of special linear groups

Let $i\geq 0$ and $n\geq 1$. The codimension-$i$ rational cohomology of $\operatorname{SL}_n(\mathbb Z)$ is $\operatorname{H}^{\binom{n}{2}-i}(\operatorname{SL}_n(\mathbb Z);\mathbb Q)$.

Church–Farb–Putman conjecture. The codimension-$i$ cohomology of $\operatorname{SL}_n(\mathbb Z)$ vanishes for $n\geq i+2$; equivalently,

$$\operatorname{H}^{i}(\operatorname{SL}_n(\mathbb Z);\mathbb Q)\cong 0$$

for $i\geq \binom{n}{2}-n+2$.

This conjecture predicts a substantially larger high-degree vanishing range for the rational cohomology of $\operatorname{SL}_n(\mathbb Z)$ than the general Borel–Serre bound. Its resolution is not established in the supplied text.