2007/06/25 by Sean Sather-Wagstaff, Sather-Wagstaff, Sean, Tirdad Sharif +3
Mathematics · #13D02 #13D05 #13D07 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0706.3635
openalex publication_date 2007/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.