Grade and Cohen-Macaulayness for DG-modules
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908850043486208 |
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| author | Ning, Yuancheng Yang, Xiaoyan |
| author_facet | Ning, Yuancheng Yang, Xiaoyan |
| contents | We establish an inequality relating the projective dimension of a DG-module in $\mathrm{D}^\mathrm{b}_\mathrm{f}(A)$ to its grade and introduce the concept of perfect DG-modules as a natural generalization of perfect modules. It is proved that a DG-module $M$ over a local Cohen-Macaulay DG-ring with constant amplitude is Cohen-Macaulay if and only if $M$ is perfect and $\mathrm{amp}M \leq \mathrm{amp}\mathrm{R}Γ_{\bar{\mathfrak{m}}}(M)$. An affirmative answer is provided to Conjecture 2.11 of Yoshida [J. Pure Appl. Algebra 123 (1998) 313--326]. We also study the grade of DG-modules with finite injective dimension and examine the preservation of Cohen-Macaulayness under tensor products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20617 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Grade and Cohen-Macaulayness for DG-modules Ning, Yuancheng Yang, Xiaoyan Commutative Algebra We establish an inequality relating the projective dimension of a DG-module in $\mathrm{D}^\mathrm{b}_\mathrm{f}(A)$ to its grade and introduce the concept of perfect DG-modules as a natural generalization of perfect modules. It is proved that a DG-module $M$ over a local Cohen-Macaulay DG-ring with constant amplitude is Cohen-Macaulay if and only if $M$ is perfect and $\mathrm{amp}M \leq \mathrm{amp}\mathrm{R}Γ_{\bar{\mathfrak{m}}}(M)$. An affirmative answer is provided to Conjecture 2.11 of Yoshida [J. Pure Appl. Algebra 123 (1998) 313--326]. We also study the grade of DG-modules with finite injective dimension and examine the preservation of Cohen-Macaulayness under tensor products. |
| title | Grade and Cohen-Macaulayness for DG-modules |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2602.20617 |