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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2503.22217 |
| Etiquetas: |
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- 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.