Admissible subcategories of noncommutative curves
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915420666068992 |
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| author | Robotis, Antonios-Alexandros |
| author_facet | Robotis, Antonios-Alexandros |
| contents | We study admissible subcategories of the derived categories of smooth noncommutative (nc) curves as classified by Reiten-van den Bergh. We prove that any admissible subcategory of the derived category of a smooth nc curve is again the derived category of a smooth nc curve. We use this result to classify semiorthogonal decompositions in derived categories of nc curves. The results obtained imply that phantom categories do not exist in these cases. As a further application, we prove an extension of the Bondal-Orlov reconstruction theorem to the case of orbifold curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06967 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Admissible subcategories of noncommutative curves Robotis, Antonios-Alexandros Algebraic Geometry Category Theory Representation Theory 14A30 18G80 We study admissible subcategories of the derived categories of smooth noncommutative (nc) curves as classified by Reiten-van den Bergh. We prove that any admissible subcategory of the derived category of a smooth nc curve is again the derived category of a smooth nc curve. We use this result to classify semiorthogonal decompositions in derived categories of nc curves. The results obtained imply that phantom categories do not exist in these cases. As a further application, we prove an extension of the Bondal-Orlov reconstruction theorem to the case of orbifold curves. |
| title | Admissible subcategories of noncommutative curves |
| topic | Algebraic Geometry Category Theory Representation Theory 14A30 18G80 |
| url | https://arxiv.org/abs/2312.06967 |