Comparison of relative cohomology theories with respect to semidualizing modules

By Sean Sather-Wagstaff, Tirdad Sharif, D. White. 2007

76 citations recorded by the source corpus.

We compare and contrast various relative cohomology theories that arise from resolutions involving semidualizing modules. We prove a general 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 comparison 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/91475e7cf4cacb660172960c82d2c4288d6d3eac

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Homological aspects of semidualizing modules (2007, background): “These connections are used in [9] to distinguish between several different relative cohomology theories.”
Tate cohomology with respect to semidualizing modules (2009, methodology): “This paper investigates Tate cohomology of objects in abelian categories, inspired by the work of Avramov and Martsinkovsky [3] and building from our own works [19,17,18].”