Strong uniqueness of enhancements for the dual numbers: a case study
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910946348236800 |
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| author | Canonaco, Alberto Neeman, Amnon Stellari, Paolo |
| author_facet | Canonaco, Alberto Neeman, Amnon Stellari, Paolo |
| contents | We prove that the bounded and bounded below derived categories of (all) modules over the dual numbers have strongly unique (dg) enhancements. To this end we relate those categories to the category of sequences of vector spaces, which allows a complete classification of indecomposable objects. Along the way we also prove that all the derived categories of any hereditary category have strongly unique enhancements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong uniqueness of enhancements for the dual numbers: a case study Canonaco, Alberto Neeman, Amnon Stellari, Paolo Algebraic Geometry Commutative Algebra Category Theory We prove that the bounded and bounded below derived categories of (all) modules over the dual numbers have strongly unique (dg) enhancements. To this end we relate those categories to the category of sequences of vector spaces, which allows a complete classification of indecomposable objects. Along the way we also prove that all the derived categories of any hereditary category have strongly unique enhancements. |
| title | Strong uniqueness of enhancements for the dual numbers: a case study |
| topic | Algebraic Geometry Commutative Algebra Category Theory |
| url | https://arxiv.org/abs/2505.10374 |