Admissible subcategories and metric techniques
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916693052227584 |
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| author | Rahul, Kabeer Manali |
| author_facet | Rahul, Kabeer Manali |
| contents | In this work, we provide a way of constructing new semiorthogonal decompositions using metric techniques (à la Neeman). Given a semiorthogonal decomposition on a category with a special kind of metric, which we call a compressible metric, we can construct new semiorthogonal decomposition on a category constructed from the given one using the aforementioned metric. In the algebro-geometric setting, this gives us a way of producing new semiorthogonal decompositions on various small triangulated categories associated to a scheme, if we are given one. In the general setting, the work is related to that of Sun-Zhang, while its applications to algebraic geometry are related to the work of Bondarko and Kuznetsov-Shinder. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11772 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Admissible subcategories and metric techniques Rahul, Kabeer Manali Algebraic Geometry Category Theory 14A30 (primary), 18G80 In this work, we provide a way of constructing new semiorthogonal decompositions using metric techniques (à la Neeman). Given a semiorthogonal decomposition on a category with a special kind of metric, which we call a compressible metric, we can construct new semiorthogonal decomposition on a category constructed from the given one using the aforementioned metric. In the algebro-geometric setting, this gives us a way of producing new semiorthogonal decompositions on various small triangulated categories associated to a scheme, if we are given one. In the general setting, the work is related to that of Sun-Zhang, while its applications to algebraic geometry are related to the work of Bondarko and Kuznetsov-Shinder. |
| title | Admissible subcategories and metric techniques |
| topic | Algebraic Geometry Category Theory 14A30 (primary), 18G80 |
| url | https://arxiv.org/abs/2504.11772 |