Tate (co)homology via pinched complexes

DOI10.1090/S0002-9947-2013-05746-7zbMath1326.18008arXiv1105.2286OpenAlexW1976826728MaRDI QIDQ5402106

David A. Jorgensen, Lars Winther Christensen

Publication date: 5 March 2014

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.2286

zbMATH Keywords

balancednessTate cohomologyTate homologytotal acyclicity

Mathematics Subject Classification ID

Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Homological functors on modules of commutative rings (Tor, Ext, etc.) (13D07) Syzygies, resolutions, complexes in associative algebras (16E05) Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) (18G15)

Related Items (25)

Tate homology of modules of finite Gorenstein flat dimension. ⋮ Vanishing of Tate homology -- an application of stable homology for complexes ⋮ Vanishing of Avramov obstructions for products of sequentially transverse ideals ⋮ Homological independence of infinite syzygies ⋮ Maximal Cohen-Macaulay tensor products ⋮ Balance in complete cohomology. ⋮ Avramov-Martsinkovsky type exact sequences with \(\mathrm {Tor}\) functors ⋮ Balance of Tate cohomology in triangulated categories ⋮ Gorenstein injective sheaves ⋮ Gorenstein rings via homological dimensions, and symmetry in vanishing of Ext and Tate cohomology ⋮ Remarks on balance for Tate and generalized Tate (co)homology ⋮ Stable homology over associative rings ⋮ Tate-Hochschild homology and cohomology of Frobenius algebras. ⋮ Stable local cohomology ⋮ Vanishing of Tate homology and depth formulas over local rings ⋮ HOMOLOGY THEORIES FOR COMPLEXES BASED ON FLATS ⋮ Tate homology of modules based on Tate \(\mathcal {F}_C\)-resolutions ⋮ Tate homology with respect to cotorsion pairs ⋮ Gorenstein \(FI\)-flat dimension and Tate homology ⋮ Strongly Gorenstein Flat Dimensions of Complexes ⋮ Balance of complete cohomology in extriangulated categories ⋮ Homology theories and Gorenstein dimensions for complexes ⋮ On tensor products of complete resolutions ⋮ Gorenstein \(n\)-flat dimension and Tate homology. ⋮ Relative and Tate homology with respect to semidualizing modules

Cites Work

• Vanishing of Tate homology and depth formulas over local rings
• On Gorenstein projective, injective and flat dimensions -- a functorial description with applications
• Homological dimensions of unbounded complexes
• Equivariant Tate-Vogel homology
• Products in negative cohomology
• Complete cohomology for arbitrary rings using injectives
• Tate cohomology for arbitrary groups via satellites
• On the vanishing of \(\lim_{(i)}\)
• Critères de platitude et de projectivité. Techniques de platification d'un module. (Criterial of flatness and projectivity. Technics of flatification of a module.)
• ABSOLUTE, RELATIVE, AND TATE COHOMOLOGY OF MODULES OF FINITE GORENSTEIN DIMENSION
• Cohomology theories based on Gorenstein injective modules
• Absolute, Gorenstein, and Tate Torsion Modules
• Gorenstein projective dimension for complexes

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