Comparison of relative cohomology theories with respect to semidualizing modules
S Sather-Wagstaff, T Sharif, D White - Mathematische Zeitschrift, 2010 - Springer
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 …
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 …