Strong generation for module categories
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912525627424768 |
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| author | Dey, Souvik Lank, Pat Takahashi, Ryo |
| author_facet | Dey, Souvik Lank, Pat Takahashi, Ryo |
| contents | This article investigates strong generation within the module category of a commutative Noetherian ring. We establish a criterion for such rings to possess strong generators within their module category, addressing a question raised by Iyengar and Takahashi. As a consequence, this not only demonstrates that any Noetherian quasi-excellent ring of finite Krull dimension satisfies this criterion, but applies to rings outside this class. Additionally, we identify explicit strong generators within the module category for rings of prime characteristic, and establish upper bounds on Rouquier dimension in terms of classical numerical invariants for modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13675 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strong generation for module categories Dey, Souvik Lank, Pat Takahashi, Ryo Commutative Algebra 13D09 (primary), 13C60, 13D05, 13D02, 13F40 This article investigates strong generation within the module category of a commutative Noetherian ring. We establish a criterion for such rings to possess strong generators within their module category, addressing a question raised by Iyengar and Takahashi. As a consequence, this not only demonstrates that any Noetherian quasi-excellent ring of finite Krull dimension satisfies this criterion, but applies to rings outside this class. Additionally, we identify explicit strong generators within the module category for rings of prime characteristic, and establish upper bounds on Rouquier dimension in terms of classical numerical invariants for modules. |
| title | Strong generation for module categories |
| topic | Commutative Algebra 13D09 (primary), 13C60, 13D05, 13D02, 13F40 |
| url | https://arxiv.org/abs/2307.13675 |