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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.15230 |
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| _version_ | 1866912385449590784 |
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| author | Baumann, Thilo |
| author_facet | Baumann, Thilo |
| contents | We show that Kuznetsov--Shinder's notion of deformation absorption of singularities leads to a new approach for studying the bounded derived category of a hereditary order on a curve. The starting point is a hereditary order which can be interpreted as a smoothing of the finite-dimensional algebra obtained from the restriction to a ramified point. We construct a triangulated subcategory inside the derived category of this finite-dimensional algebra which provides a deformation absorption of singularities. This allows us to obtain a semiorthogonal decomposition of the bounded derived category of the hereditary order, which is in addition linear over the base. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15230 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categorical absorption for hereditary orders Baumann, Thilo Algebraic Geometry Representation Theory We show that Kuznetsov--Shinder's notion of deformation absorption of singularities leads to a new approach for studying the bounded derived category of a hereditary order on a curve. The starting point is a hereditary order which can be interpreted as a smoothing of the finite-dimensional algebra obtained from the restriction to a ramified point. We construct a triangulated subcategory inside the derived category of this finite-dimensional algebra which provides a deformation absorption of singularities. This allows us to obtain a semiorthogonal decomposition of the bounded derived category of the hereditary order, which is in addition linear over the base. |
| title | Categorical absorption for hereditary orders |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2505.15230 |