Compactness of the Alexandrov topology of maximal Cohen-Macaulay modules
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916086819061760 |
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| author | Kimura, Kaito |
| author_facet | Kimura, Kaito |
| contents | Let $R$ be a Cohen-Macaulay local ring. In this paper, we first describe the radicals of annihilators of stable categories of maximal Cohen-Macaulay $R$-modules. We then prove that the Alexandrov topology of the stable category of maximal Cohen-Macaulay $R$-modules is compact provided that the completion of $R$ has an isolated singularity. Finally, we consider the case of a hypersurface of countable CM-representation type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compactness of the Alexandrov topology of maximal Cohen-Macaulay modules Kimura, Kaito Commutative Algebra Representation Theory 13C60, 13C14, 54A05 Let $R$ be a Cohen-Macaulay local ring. In this paper, we first describe the radicals of annihilators of stable categories of maximal Cohen-Macaulay $R$-modules. We then prove that the Alexandrov topology of the stable category of maximal Cohen-Macaulay $R$-modules is compact provided that the completion of $R$ has an isolated singularity. Finally, we consider the case of a hypersurface of countable CM-representation type. |
| title | Compactness of the Alexandrov topology of maximal Cohen-Macaulay modules |
| topic | Commutative Algebra Representation Theory 13C60, 13C14, 54A05 |
| url | https://arxiv.org/abs/2401.04987 |