Descending strong generation in algebraic geometry
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910823092322304 |
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| author | De Deyn, Timothy Lank, Pat Rahul, Kabeer Manali |
| author_facet | De Deyn, Timothy Lank, Pat Rahul, Kabeer Manali |
| contents | We formalize the main approach for showing Zariski descent-type statements for strong generation of triangulated categories associated to algebro-geometric objects. This recovers various known statements in the literature. As applications we show that strong generation for the singularity category of a Noetherian separated scheme is Zariski local and obtain a strong generation result for the bounded derived category of a Noetherian concentrated algebraic stacks with finite diagonal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Descending strong generation in algebraic geometry De Deyn, Timothy Lank, Pat Rahul, Kabeer Manali Algebraic Geometry Commutative Algebra 14A30 (primary), 18G80, 14A22 We formalize the main approach for showing Zariski descent-type statements for strong generation of triangulated categories associated to algebro-geometric objects. This recovers various known statements in the literature. As applications we show that strong generation for the singularity category of a Noetherian separated scheme is Zariski local and obtain a strong generation result for the bounded derived category of a Noetherian concentrated algebraic stacks with finite diagonal. |
| title | Descending strong generation in algebraic geometry |
| topic | Algebraic Geometry Commutative Algebra 14A30 (primary), 18G80, 14A22 |
| url | https://arxiv.org/abs/2502.08629 |