2 problems

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

Let $\ell$ be a prime number. Let $K$ be a number field with $\zeta_\ell\in K$, and let $S$ be a finite set of places containing the infinite places and the places over $\ell$. The…