Group cohomology and field theory
by
Jan Minac
The University of Western Ontario
Coauthors: Alejandro Adem (University of Wisconsin-Madison), Dikran Karagueuzian (University of Wisconsin-Madison)

I shall discuss the group cohomology of some Galois groups determined by the Witt rings of quadratic forms. I shall describe the mod 2 cohomology of a Galois group called the W group of a field F attached to a field F of a characteristic not equal to two. It will be shown that this group contains a Galois cohomology of a field F and also other interesting invariants of a field F. Further, there will be constructed some topological space endowed with the action of an elementary abelian group, such that the computation of the cohomology of our W group of F reduces to calculating the equivariant cohomology of our constructed topological space with respect to our action of the elementary abelian group mentioned above. In the case of a field which is not formally real, this amounts to computing the cohomology of an explicit Euclidean space form. I shall provide a number of examples and some combinatorial computation for the cohomology of the free W groups. The main heros of this story are circles, groups and fields.

Date received: April 25, 1999