Local Cohen–Macaulay DG-Modules

Let A be a commutative noetherian local DG-ring with bounded cohomology. For local Cohen–Macaulay DG-modules with constant amplitude, we obtain an explicit formula for the sequential depth, show that Cohen–Macaulayness is stable under localization and give several equivalent definitions of maximal l...

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Bibliographic Details
Published in:Applied categorical structures 2023-02, Vol.31 (1), Article 8
Main Authors: Yang, Xiaoyan, Li, Yanjie
Format: Article
Language:English
Subjects:
Convex and Discrete Geometry
Geometry
Homology
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Modules
Rings (mathematics)
Theory of Computation
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Summary:Let A be a commutative noetherian local DG-ring with bounded cohomology. For local Cohen–Macaulay DG-modules with constant amplitude, we obtain an explicit formula for the sequential depth, show that Cohen–Macaulayness is stable under localization and give several equivalent definitions of maximal local Cohen–Macaulay DG-modules over local Cohen–Macaulay DG-rings. We also provide some characterizations of Gorenstein DG-rings by projective and injective dimensions of DG-modules.
ISSN:0927-2852
1572-9095
DOI:10.1007/s10485-022-09703-y