### 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
H^{2}_{cts}(SL_{n}(k[[T]]),k)
vanishes for n at least 3.

Kevin P. Knudson <knudson@math.wayne.edu>