A generalization of the Auslander-Buchsbaum formula

DOI10.1016/S0022-4049(98)00057-7zbMath0951.13010OpenAlexW2018699971WikidataQ127363768 ScholiaQ127363768MaRDI QIDQ1964128

David A. Jorgensen

Publication date: 18 December 2000

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

Full work available at URL: https://doi.org/10.1016/s0022-4049(98)00057-7

zbMATH Keywords

Tordeformationcomplete intersectionlocal ringdepth formulaAuslander-Buchsbaum formulaGolod ringfinite projective dimension

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Homological functors on modules of commutative rings (Tor, Ext, etc.) (13D07) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15)

Related Items (25)

Nonvanishing cohomology and classes of Gorenstein rings ⋮ Applications of Differential Graded Algebra Techniques in Commutative Algebra ⋮ Depth Formula via Complete Intersection Flat Dimension ⋮ Vanishing of cohomology over Gorenstein rings of small codimension ⋮ Minimal intersections and vanishing (co)homology ⋮ Modules with reducible complexity ⋮ Maximal Cohen-Macaulay tensor products ⋮ Exterior powers and Tor-persistence ⋮ Intersections of resolving subcategories and intersections of thick subcategories ⋮ Necessary conditions for the depth formula over Cohen-Macaulay local rings ⋮ Persistence of homology over commutative Noetherian rings ⋮ A study of Tate homology via the approximation theory with applications to the depth formula ⋮ On modules with self Tor vanishing ⋮ Extremal growth of Betti numbers and trivial vanishing of (co)homology ⋮ Homology over trivial extensions of commutative DG algebras ⋮ Poincaré series of modules over compressed Gorenstein local rings ⋮ Vanishing of Tor, and why we care about it ⋮ Vanishing of relative homology and depth of tensor products ⋮ Vanishing of Tate Cohomology and Gorenstein Injective Dimension ⋮ Bounds on depth of tensor products of modules ⋮ Vanishing theorems for complete intersections ⋮ Depth formulas, restricted Tor-dimension under base change ⋮ Homological dimensions of rigid modules ⋮ VANISHING OF (CO)HOMOLOGY OVER DEFORMATIONS OF COHEN-MACAULAY LOCAL RINGS OF MINIMAL MULTIPLICITY ⋮ Extensions of a dualizing complex by its ring: Commutative versions of a conjecture of Tachikawa

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