On the top dimensional cohomology groups of congruence subgroups of ${\text{SL}}_n(\mathbb{Z})$

Jeremy Miller, Peter Patzt, Andrew Putman

Let ${\Gamma }_n(p)$ be the level-$p$ principal congruence subgroup of ${\text{SL}}_n(\mathbb{Z})$. Borel-Serre proved that the cohomology of ${\Gamma }_n(p)$ vanishes above degree $\left(\genfrac{}{}{0ex}{}{n}{2}\right)$. W…