Approximable Triangulated Categories and Reflexive DG-categories
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913837673873408 |
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| author | Goodbody, Isambard Raedschelders, Theo Stevenson, Greg |
| author_facet | Goodbody, Isambard Raedschelders, Theo Stevenson, Greg |
| contents | We use the theory of approximable triangulated categories to give a condition for a proper DG-category to be reflexive in the sense of Kuznetsov and Shinder. To do this we provide another description of the completion of an approximable triangulated category under a properness assumption. We apply our results to proper schemes, proper connective DG-algebras and Azumaya algebras over proper schemes. We include an appendix by Raedschelders and Stevenson showing that proper connective DG-algebras admit finite dimensional models over any field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09461 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximable Triangulated Categories and Reflexive DG-categories Goodbody, Isambard Raedschelders, Theo Stevenson, Greg Algebraic Geometry Representation Theory We use the theory of approximable triangulated categories to give a condition for a proper DG-category to be reflexive in the sense of Kuznetsov and Shinder. To do this we provide another description of the completion of an approximable triangulated category under a properness assumption. We apply our results to proper schemes, proper connective DG-algebras and Azumaya algebras over proper schemes. We include an appendix by Raedschelders and Stevenson showing that proper connective DG-algebras admit finite dimensional models over any field. |
| title | Approximable Triangulated Categories and Reflexive DG-categories |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2411.09461 |