A model structure approach to the Tate-Vogel cohomology

DOI10.1016/j.jpaa.2015.11.004zbMath1373.16026OpenAlexW2244076003MaRDI QIDQ908325

Jiangsheng Hu, Nan Qing Ding

Publication date: 4 February 2016

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2015.11.004

zbMATH Keywords

finitistic dimension conjectureGorenstein flat dimensionTate-Vogel cohomology

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Syzygies, resolutions, complexes in associative algebras (16E05) Homological dimension (category-theoretic aspects) (18G20) Chain complexes (category-theoretic aspects), dg categories (18G35)

Related Items

Triangulated equivalence between a homotopy category and a triangulated quotient category, Complete cohomology for complexes with finite Gorenstein AC-projective dimension, Relative singularity categories with respect to Gorenstein flat modules, A refinement of Gorenstein flat dimension via the flat-cotorsion theory, Tate cohomology for complexes with finite Gorenstein AC-injective dimension, Relative homological dimensions and Tate cohomology of complexes with respect to cotorsion pairs, Buchweitz’s equivalences for Gorenstein flat modules with respect to semidualizing modules

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cohomology of sheaves
• Model structures on exact categories
• Comparison of relative cohomology theories with respect to semidualizing modules
• On Gorenstein projective, injective and flat dimensions -- a functorial description with applications
• Cohomology theories for complexes
• On a question of Gillespie
• Gorenstein flat dimension of complexes.
• Homological dimensions of unbounded complexes
• Equivariant Tate-Vogel homology
• Products in negative cohomology
• Tate cohomology for arbitrary groups via satellites
• Gorenstein homological dimensions.
• Gorenstein dimensions
• Flat covers of modules
• Cotorsion pairs, model category structures, and representation theory
• Gorenstein injective and projective modules
• Relative homological algebra
• Homological dimensions in cotorsion pairs.
• On the finitistic dimension conjecture. II: Related to finite global dimension
• Stable cohomology over local rings
• Cotorsion pairs and degreewise homological model structures
• Approximations and endomorphism algebras of modules.
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• On the ubiquity of Gorenstein rings
• A model structure approach to the finitistic dimension conjectures
• Cotorsion pairs and model structures on Ch(R)
• Tilting theory and the finitistic dimension conjectures
• ABSOLUTE, RELATIVE, AND TATE COHOMOLOGY OF MODULES OF FINITE GORENSTEIN DIMENSION
• ALL MODULES HAVE FLAT COVERS
• Homological Dimension in Local Rings
• Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
• Rings Over Which the Class of Gorenstein Flat Modules is Closed Under Extensions
• On rings with finite self-injective dimension
• Rings with finite Gorenstein injective dimension
• DUALIZING MODULES AND n-PERFECT RINGS
• The flat model structure on 𝐂𝐡(𝐑)
• APPLICATIONS OF COTORSION PAIRS
• The finitistic dimension conjectures -- a tale of 3.5 decades
• Gorenstein injective covers and envelopes over noetherian rings
• Character modules, dimension and purity
• the stable derived category of a noetherian scheme
• Gorenstein projective dimension for complexes
• Tilting Cotorsion Pairs