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arXiv · 2604.05437

A characterization of Cohen-Macaulay rings in terms of levels of perfect complexes

Naoya Hiramatsu·Yuki Mifune·Ryo Takahashi
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Abstract

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 $R$.

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Naoya Hiramatsu, Yuki Mifune, Ryo Takahashi. 2026-04-07. A characterization of Cohen-Macaulay rings in terms of levels of perfect complexes. https://arxiv.org/abs/2604.05437

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