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arXiv · 2401.11153

A generalization of the dimension and radius of a subcategory of modules and its applications

Yuki Mifune
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Abstract

Let $R$ be a commutative noetherian local ring and denote by $\operatorname{mod} R$ the category of finitely generated $R$-modules. In this paper, we give some evaluations of the singular locus of $R$ and annihilators of Tor and Ext from a viewpoint of the finiteness of dimensions/radii of full subcategories of $\operatorname{mod} R$. As an application, we recover a theorem of Dey and Takahashi when $R$ is Cohen--Macaulay. Moreover, we obtain the divergence of the dimensions of specific full subcategories of $\operatorname{mod} R$ in non-Cohen--Macaulay case.

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Yuki Mifune. 2024-01-20. A generalization of the dimension and radius of a subcategory of modules and its applications. https://arxiv.org/abs/2401.11153

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