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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2401.11153 |
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| _version_ | 1866909078285975552 |
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| author | Mifune, Yuki |
| author_facet | Mifune, Yuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A generalization of the dimension and radius of a subcategory of modules and its applications Mifune, Yuki Commutative Algebra Representation Theory 13C60, 13D07 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. |
| title | A generalization of the dimension and radius of a subcategory of modules and its applications |
| topic | Commutative Algebra Representation Theory 13C60, 13D07 |
| url | https://arxiv.org/abs/2401.11153 |