Relative completions and the cohomology of linear groups over local rings, by Kevin P. Knudson

In this paper we discuss the completion of various groups relative to a Zariski dense representation in a reductive group S. This is a generalization of the well-known Malcev completion. We use this construction to study the second continuous cohomology of linear groups over various rings. For example, we show that if k is a number field, then the group H2cts(SLn(k[[T]]),k) vanishes for n at least 3.

Kevin P. Knudson <>