The Cohen-Macaulay property in derived commutative algebra

DOI10.1090/tran/8099zbMath1457.13023arXiv1902.06771OpenAlexW3004121820MaRDI QIDQ5125167

Liran Shaul

Publication date: 5 October 2020

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

Full work available at URL: https://arxiv.org/abs/1902.06771

zbMATH Keywords

differential graded ringsCohen Macaulay modules

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) (13D03) Local cohomology and commutative rings (13D45) Differential graded algebras and applications (associative algebraic aspects) (16E45) Cohen-Macaulay modules (13C14) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Derived categories, triangulated categories (18G80)

Related Items (9)

Singularity categories via the derived quotient ⋮ Depth and dimension for triangulated categories ⋮ COSUPPORT FOR COMPACTLY GENERATED TRIANGULATED CATEGORIES ⋮ Cohomological dimension of DG-modules ⋮ Sequence-regular commutative DG-rings ⋮ Koszul complexes over Cohen-Macaulay rings ⋮ Homological identities and dualizing complexes of commutative differential graded algebras ⋮ Open loci results for commutative DG-rings ⋮ Local Cohen-Macaulay DG-modules

Cites Work

• Unnamed Item
• Krull dimension for differential graded algebras
• Dimension projective finie et cohomologie locale. Applications à la demonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck
• Duality in algebra and topology
• The squaring operation for commutative DG rings
• Existence of dualizing complexes
• Gorenstein spaces
• Derived functors of \(I\)-adic completion and local homology
• Bounded complexes of flat modules
• Cohen-Macaulay properties of ring homomorphisms
• Gorenstein differential graded algebras
• Injective DG-modules over non-positive DG-rings
• On the homology of completion and torsion
• Completion and torsion over commutative DG rings
• The twisted inverse image pseudofunctor over commutative DG rings and perfect base change
• Dualizing complexes and perverse sheaves on noncommutative ringed schemes
• 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
• On arithmetic Macaulayfication of Noetherian rings
• Local cohomology and support for triangulated categories
• Locally Gorenstein Homomorphisms
• Sequences for complexes
• Sequences for complexes II
• Recognizing dualizing complexes
• DUALIZING DIFFERENTIAL GRADED MODULES AND GORENSTEIN DIFFERENTIAL GRADED ALGEBRAS
• Colocalizing subcategories and cosupport
• Amplitude inequalities for Differential Graded modules

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