A characterization of Cohen-Macaulay rings in terms of levels of perfect complexes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915920043048960 |
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| author | Hiramatsu, Naoya Mifune, Yuki Takahashi, Ryo |
| author_facet | Hiramatsu, Naoya Mifune, Yuki Takahashi, Ryo |
| contents | Let $R$ be a commutative noetherian ring, and let $C$ be a semidualizing $R$-module. In this paper, we study levels of bounded complexes of finitely generated $R$-modules with respect to the full subcategory $\mathsf{G}_{C}(R)$ consisting of Gorenstein $C$-projective $R$-modules. Our main result provides a characterization of the Cohen-Macaulayness of $R$ in terms of the finiteness of levels of perfect complexes with respect to $\mathsf{G}_{C}(R)$. This recovers a recent theorem of Christensen, Kekkou, Lyle and Soto Levins on the Gorensteinness of $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05437 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A characterization of Cohen-Macaulay rings in terms of levels of perfect complexes Hiramatsu, Naoya Mifune, Yuki Takahashi, Ryo Commutative Algebra Representation Theory 13D09, 13H10 Let $R$ be a commutative noetherian ring, and let $C$ be a semidualizing $R$-module. In this paper, we study levels of bounded complexes of finitely generated $R$-modules with respect to the full subcategory $\mathsf{G}_{C}(R)$ consisting of Gorenstein $C$-projective $R$-modules. Our main result provides a characterization of the Cohen-Macaulayness of $R$ in terms of the finiteness of levels of perfect complexes with respect to $\mathsf{G}_{C}(R)$. This recovers a recent theorem of Christensen, Kekkou, Lyle and Soto Levins on the Gorensteinness of $R$. |
| title | A characterization of Cohen-Macaulay rings in terms of levels of perfect complexes |
| topic | Commutative Algebra Representation Theory 13D09, 13H10 |
| url | https://arxiv.org/abs/2604.05437 |