Localization theorems for weakly approximable triangulated categories
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910123528552448 |
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| author | Sun, Yongliang Zhang, Jinbi Zhang, Yaohua |
| author_facet | Sun, Yongliang Zhang, Jinbi Zhang, Yaohua |
| contents | Weakly approximable triangulated categories, introduced by Neeman, provide a powerful framework for studying localization phenomena in triangulated categories. In this paper, we establish new localization theorems showing that, under mild assumptions, a recollement of weakly approximable triangulated categories induces short exact sequences on several natural triangulated subcategories as well as on the associated (big) singularity categories. As applications, we illustrate our results in the derived categories of rings, DG algebras, and schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04954 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Localization theorems for weakly approximable triangulated categories Sun, Yongliang Zhang, Jinbi Zhang, Yaohua Representation Theory Category Theory Rings and Algebras 18G80, 16E35 Weakly approximable triangulated categories, introduced by Neeman, provide a powerful framework for studying localization phenomena in triangulated categories. In this paper, we establish new localization theorems showing that, under mild assumptions, a recollement of weakly approximable triangulated categories induces short exact sequences on several natural triangulated subcategories as well as on the associated (big) singularity categories. As applications, we illustrate our results in the derived categories of rings, DG algebras, and schemes. |
| title | Localization theorems for weakly approximable triangulated categories |
| topic | Representation Theory Category Theory Rings and Algebras 18G80, 16E35 |
| url | https://arxiv.org/abs/2402.04954 |