Associated primes for cohomology modules

Let G be a finite group acting linearly on a finite dimensional vector space V defined over a field k of characteristic p, where p is assumed to divide the group order. Let R := S(V *) be the symmetric algebra of the dual on which G acts naturally by algebra automorphisms. We study the R^G-modules Hⁱ(G, R) for i > 0. In particular we give a formula which describes the annihilator of a general element of Hⁱ(G, R) in terms of the relative transfer ideals of R^G, and consequently prove that the associated primes of these cohomology modules are equal to the radicals of certain relative transfer ideals. Received: 5 June 2008