Gorenstein cohomology in abelian categories

DOI10.1215/kjm/1250271384zbMath1172.18004arXiv0706.3739OpenAlexW2962877514MaRDI QIDQ1025735

Tirdad Sharif, Diana White, Sean K. Sather-Wagstaff

Publication date: 23 June 2009

Published in: Journal of Mathematics of Kyoto University (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.3739

zbMATH Keywords

balanceAuslander--Buchweitz approximationsrelative perfection

Mathematics Subject Classification ID

Homological functors on modules of commutative rings (Tor, Ext, etc.) (13D07) Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) (18G15) Homological dimension (category-theoretic aspects) (18G20) Abelian categories, Grothendieck categories (18E10) Relative homological algebra, projective classes (category-theoretic aspects) (18G25)

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Complete cohomology for complexes with finite Gorenstein AC-projective dimension ⋮ Tate cohomology with respect to semidualizing modules ⋮ Generalized Tate cohomology and Avramov–Martsinkovsky type sequences ⋮ Balance functors and relative tilting modules ⋮ Balance for relative cohomology of complexes ⋮ Gorenstein projective dimension with respect to a semidualizing module ⋮ Preservation of quasi-isomorphisms of complexes ⋮ Remarks on balance for Tate and generalized Tate (co)homology ⋮ Relative cohomology and generalized Tate cohomology ⋮ Relative cohomology of complexes ⋮ Gorenstein cohomology of N-complexes ⋮ Relative cohomology of complexes based on cotorsion pairs ⋮ Duality pairs induced by Gorenstein projective modules with respect to semidualizing modules ⋮ Tate homology with respect to cotorsion pairs ⋮ Relative derived categories with respect to subcategories ⋮ On Balance for Relative Homology ⋮ SEMIDUALIZING MODULES AND RELATED MODULES ⋮ Balance for relative (co)homology in abelian categories

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