Permutation complexes for profinite groups. (Q863617)

The aim of the paper is to develop the cohomology theory of profinite groups along the lines of that done for discrete groups. In particular, the author is interested in constructing an algebraic analogue of a finite dimensional contractible space on which the group acts with finite stabilizers and in developing its consequences. This requires a review of the basic module theory behind the cohomology of profinite groups. Particular attention is given to permutation modules and the Brauer quotient, adapting some results of Swan on the cohomology of fixed point sets and the work of Bouc on complexes of these modules. This enables the author to formulate precisely the complexes he want and their properties. He then defines the Tate-Farrell cohomology for a profinite group of finite virtual cohomological dimension and uses the complexes to develop its properties. There are applications to questions about the finiteness of the number of conjugacy classes of finite subgroups and to the local cohomology of the group.