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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2503.22217 |
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| _version_ | 1866911455875432448 |
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| author | Chen, Mingfa |
| author_facet | Chen, Mingfa |
| contents | In this paper we introduce a local-refinement procedure to investigate finite t-stabilities on a triangulated category, and show a direct sufficient condition for a finite t-stability to be finite finest. We classify all finite finest t-stabilities for certain triangulated categories, including those from the projective plane, weighted projective lines, and finite acyclic quivers. As applications, we obtain a simple classification of semi-orthogonal decompositions (SOD) for these categories. Furthermore, we study the connectedness of SODs by a reduction method and give an easily verified criterion for it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-orthogonal decompositions via t-stabilities Chen, Mingfa Category Theory In this paper we introduce a local-refinement procedure to investigate finite t-stabilities on a triangulated category, and show a direct sufficient condition for a finite t-stability to be finite finest. We classify all finite finest t-stabilities for certain triangulated categories, including those from the projective plane, weighted projective lines, and finite acyclic quivers. As applications, we obtain a simple classification of semi-orthogonal decompositions (SOD) for these categories. Furthermore, we study the connectedness of SODs by a reduction method and give an easily verified criterion for it. |
| title | Semi-orthogonal decompositions via t-stabilities |
| topic | Category Theory |
| url | https://arxiv.org/abs/2503.22217 |