Vanishing of cohomology over Cohen-Macaulay rings

DOI10.1007/s00229-012-0540-7zbMath1255.13009arXiv1006.1006OpenAlexW1971111591MaRDI QIDQ692612

Henrik Holm, Lars Winther Christensen

Publication date: 6 December 2012

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.1006

zbMATH Keywords

Cohen-Macaulay ringsExtAC rings

Mathematics Subject Classification ID

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

Related Items (11)

The Auslander-Reiten Conjecture for Group Rings ⋮ Descent via Koszul extensions ⋮ On the finiteness of Ext-indices of ring extensions ⋮ On maximal ideals of the polynomial ring and some conjectures on Ext-index of rings ⋮ Auslander-Reiten conjecture and Auslander-Reiten duality ⋮ On modules with self Tor vanishing ⋮ On the Auslander–Reiten conjecture for Cohen–Macaulay rings and path algebras ⋮ Extremal growth of Betti numbers and trivial vanishing of (co)homology ⋮ Finitistic extension degree. ⋮ On the vanishing of self extensions over Cohen-Macaulay local rings ⋮ Two generalizations of Auslander-Reiten duality and applications

Cites Work

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• Algebras that satisfy Auslander's condition on vanishing of cohomology.
• Homological dimensions of unbounded complexes
• Structure of local homomorphisms
• Restricted homological dimensions and Cohen-Macaulayness
• The classification of homogeneous Cohen-Macaulay rings of finite representation type
• Two theorems about maximal Cohen-Macaulay modules
• Nonvanishing cohomology and classes of Gorenstein rings
• Locally complete intersection homomorphisms and a conjecture of Quillen on the vanishing of cotangent homology
• The homological theory of maximal Cohen-Macaulay approximations
• Gorenstein local homomorphisms
• Isomorphims between complexes with applications to the homological theory of modules.
• Symmetry in the vanishing of Ext over Gorenstein rings
• Characterization of Completions of Unique Factorization Domains

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