Cohomology rings of various classes of groups have curious duality properties expressed in terms of their local cohomology [2, 3, 12, 4, 5, 6]. We formulate a purely algebraic form of this duality, and investigate its consequences. It is obvious that a Cohen-Macaulay ring of this sort is automatically Gorenstein, and that its Hilbert series therefore satisfies a functional equation, and our mai...
