An analogue of Brumer's criterion for hypercohomology groups and class formations. (Q1775457)

The strict cohomological dimension \(\text{scd}_pG\) of a profinite group \(G\) is the smallest integer \(n\) such that the \(p\)-primary component of \(H^{n+1}(G,M)\) vanishes for all discrete \(G\)-modules \(M\), where \(p\) is a prime number. \textit{A. Brumer} [J. Algebra 4, 442-470 (1966; Zbl 0146.04702)] gave a useful criterion for determining \(\text{scd}_pG\) for a class formation \((G,A)\). In a previous paper [Invent. Math. 101, No. 3, 705-715 (1990; Zbl 0751.11055)] the author generalized the theory of class formations, including complexes and hypercohomology groups. In the present paper he generalizes the Brumer criterion to the case of such class formations.