Classifying KE-closed subcategories over a commutative noetherian ring
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916937637822464 |
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| author | Kobayashi, Toshinori Saito, Shunya |
| author_facet | Kobayashi, Toshinori Saito, Shunya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05767 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classifying KE-closed subcategories over a commutative noetherian ring Kobayashi, Toshinori Saito, Shunya Commutative Algebra Representation Theory 13C60 (Primary), 13D02, 18E10 (Secondary) 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. |
| title | Classifying KE-closed subcategories over a commutative noetherian ring |
| topic | Commutative Algebra Representation Theory 13C60 (Primary), 13D02, 18E10 (Secondary) |
| url | https://arxiv.org/abs/2509.05767 |