Modular representations and the cohomology of finite groups (Q1821192)

It was proved by \textit{D. L. Rector} [J. Pure Appl. Algebra \(\underset \tilde{} 4\), 137-158 (1974; Zbl 0323.18009)] that for G a finite group, the flat bundle map induces a natural, continuous isomorphism R \({\mathbb{F}}_ q(G)^{\wedge}\to K {\mathbb{F}}_ q(BG)\), where the completion on the left is by powers of the argumentation ideal. A strategy for a new proof is proposed, and this is supported by some explicit calculations for a few groups G, and by an analogous result for \({\mathbb{R}}\) and algebraically closed subfields of \({\mathbb{C}}\).