Trace forms of G-Galois algebras in virtual cohomological dimension 1 and 2

Eva Bayer-Fluckiger, Marina Monsurrò, R. Parimala and René Schoof

Vol. 217 (2004), No. 1, 29–43

DOI: 10.2140/pjm.2004.217.29

Abstract

Let G be a finite group and let k be a field of char(k)≠2. We explicitly describe the set of trace forms of G-Galois algebras over k when the virtual 2-cohomological dimension vcd₂(k) of k is at most 1. For fields with vcd₂(k) ≤ 2 we give a cohomological criterion for the orthogonal sum of a trace form of a G-Galois algebra with itself to be isomorphic to another such form.

Milestones

Received: 2 February 2003

Revised: 25 August 2003

Published: 1 November 2004