# Borel’s stable range for the cohomology of arithmetic groups

### J. Lie Theory. 29(2019) 4, 1093-1102.

In this note, we remark on the range in Borel’s theorem on the stable cohomology of the arithmetic groups Sp(2n,Z) and SO(n,n;Z). The main result improves the range stated in Borel’s original papers, an improvement that was known to Borel. The proof is a technical computation involving the Weyl group action on roots and weights.