What is the rational cohomological dimension of the lattices in $SL_n(\mathbb{Q}_p)$, where $n\geq 3$ ? A reference would be appreciated.
For the definition of "cohomological dimension of a group over ring" one can look at here: https://en.wikipedia.org/wiki/Cohomological_dimension, and the term `rational cohomological dimension' is used when the ring is taken as the field of rational numbers $\mathbb{Q}$.