Let A be a differential graded algebra with cohomology ring HA. A graded module over HA is called realisable if it is (up to direct summands) of the form HM for some differential graded A-module M . Benson, Krause and Schwede have stated a local and a global obstruction for realisability. The global obstruction is given by the Hochschild class determined by the secondary multiplication of the A...

Alexander duality is made into a functor which extends the notion for monomial ideals to any finitely generated N-graded module. The functors associated with Alexander duality provide a duality on the level of free and injective resolutions, and numerous Bass and Betti number relations result as corollaries. A minimal injective resolution of a module M is equivalent to the injective resolution ...