Relative completions and the cohomology of linear groups over local rings

Abstract

We study the completion of a group relative to a Zariski dense representation in a reductive algebraic group over a field $k$. The characteristic zero case was worked out previously by R. Hain; we extend his results to arbitrary characteristic. The primary application is to the study of the cohomology of groups such as $S{L}_n(k[[T]])$.

arXiv comment24 pages