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Paper   IPM / M / 8956
School of Mathematics
  Title:   Comparison of relative cohomology theories with respect to semidualizing modules
  Author(s):  T. Sharif (Joint with S. Sather-Wagstaff and D. White)
  Status:   Published
  Journal: Math. Z.
  Vol.:  264
  Year:  2010
  Pages:   571-600
  Supported by:  IPM
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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