Cohomology Rings of Modules

Associated primes for cohomology modules

“…It is a simple consequence of the transfer-restriction formula for cup products ( [2], Theorem 4.4.2) and the starting point for our investigations. Throughout this section, let m be a strictly positive integer.…”

“…Brief digression: Consider for a moment the cohomology ring H := H * (G, k) of a finite group G with coefficients in a field k whose characteristic divides the order of G. It is known (see, for example [2], Theorem 12.7.1) that the associated primes of the ring H take the form ker(res G E ) for certain elementary abelian subgroups E of G. Using a result of Benson ([1], Theorem 1.1), one can show this is equal to X∈χ Tr G X (H * (X, k)) where χ is the set of subgroups of G not contained in any Sylow-p-subgroup of C G (E). So the associated primes of H are also radicals of relative transfer ideals.…”