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Abstract: We compare and contrast various relative cohomology theories that arise fromresolutions involving semidualizing modules. We prove a general balance resultfor relative cohomology over a Cohen-Macaulay ring with a dualizing module, andwe demonstrate the failure of the naive version of balance one might expect forthese functors. We prove that the natural comparison morphisms between relativecohomology modules are isomorphisms in several cases, and we provide aYoneda-type description of the first relative Ext functor. Finally, we show byexample that each distinct relative cohomology construction does in fact resultin a different functor.



Author: Sean Sather-Wagstaff, Tirdad Sharif, Diana White

Source: https://arxiv.org/







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