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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.12075 |
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| _version_ | 1866915184681943040 |
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| author | Haiden, Fabian Wu, Dongjian |
| author_facet | Haiden, Fabian Wu, Dongjian |
| contents | We show that the Jordan-Hölder property fails for polarizable semiorthogonal decompositions -- those where every factor admits a Bridgeland stability condition. Counterexamples exist among Fukaya categories of surfaces and bounded derived categories of smooth projective varieties. Furthermore, we give an example of a smooth and proper pre-triangulated dg category with positive rank Grothendieck group which does not admit a stability condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12075 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A counterexample to the Jordan-Hölder property for polarizable semiorthogonal decompositions Haiden, Fabian Wu, Dongjian Representation Theory Algebraic Geometry We show that the Jordan-Hölder property fails for polarizable semiorthogonal decompositions -- those where every factor admits a Bridgeland stability condition. Counterexamples exist among Fukaya categories of surfaces and bounded derived categories of smooth projective varieties. Furthermore, we give an example of a smooth and proper pre-triangulated dg category with positive rank Grothendieck group which does not admit a stability condition. |
| title | A counterexample to the Jordan-Hölder property for polarizable semiorthogonal decompositions |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2502.12075 |