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|Paper IPM / M / 8956||
We compare and contrast various relative cohomology theories that arise from resolutions involving semidualizing modules. We prove a gen?eral balance result for relative cohomology over a Cohen-Macaulay ring with a dualizing module, and we demonstrate the failure of the naive version of balance one might expect for these functors. We prove that the natural com?parison morphisms between relative cohomology modules are isomorphisms in several cases, and we provide a Yoneda-type description of the first relative Ext functor. Finally, we show by example that each distinct relative cohomology construction does in fact result in a different functor.
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