Year: 2025
Type: preprint
Abstract: Let $\mathsf{mod} R$ denote the category of finitely generated $R$-modules for a commutative noetherian ring $R$. In this paper, we investigate KE-closed subcategories of $\mathsf{mod} R$ as a continuation of our previous work. We associate a function on $\mathrm{Spec} R$ with each KE-closed subcategory of $\mathsf{mod} R$, and show that this function completely determines the original subcategory. To classify the functions obtained from KE-closed subcategories, we introduce the notion of an $n$-Bass function for each $n\ge 0$. We obtain a bijection between the set of KE-closed subcategories and the set of $2$-Bass functions provided that $R$ is $(S_2)$-excellent in the sense of Česnavičius.
Source: arXiv (Cornell University)
Authors: Kobayashi, Toshinori, Saito, Shunya
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415053174
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