Abstract
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.
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The author would like to thank the referees for his/her valuable comments and suggestions in shaping the paper into its present form. This research was partially supported by National Natural Science Foundation of China (11901463).
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We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “Local Cohen–Macaulay DG-modules”.
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Communicated by Henning Krause.
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Yang, X., Li, Y. Local Cohen–Macaulay DG-Modules. Appl Categor Struct 31, 8 (2023). https://doi.org/10.1007/s10485-022-09703-y
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DOI: https://doi.org/10.1007/s10485-022-09703-y