Project A8: The stable cohomology of symplectic and orthogonal groups

The goal of the project is to compute the stable cohomology of the arithmetic groups from the title, primarily in the case of forms over the integers. The stable cohomology is known rationally from work of Borel, but information about torsion has remained limited to small degrees. Recent advances in hermitian K-theory allow access to this torsion far beyond this range. Part of the project is also to establish the existence of a stable part of the cohomology in the requisite generality. This is known in many cases, going back to work of Charney, but for example in the case of indefinite, odd orthogonal groups is not known even for the integers.