Triangulated categories with a compact silting object, Brown-Comenetz duality and Brown representability theorems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914331492352000 |
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| author | Chen, Xiaohu Sun, Yongliang Zhang, Yaohua |
| author_facet | Chen, Xiaohu Sun, Yongliang Zhang, Yaohua |
| contents | In this paper, we establish a dual framework for Neeman's results concerning triangulated categories with compact silting objects by employing Brown--Comenetz duality. This framework introduces an intrinsic non-compact subcategory, provides its characterization, and demonstrates representability theorems for both the low-bounded and bounded subcategories. Additionally, it elucidates how recollements are restricted to short exact sequences on the dual (non-compact) side. Several localization results and specific applications are also derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14383 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Triangulated categories with a compact silting object, Brown-Comenetz duality and Brown representability theorems Chen, Xiaohu Sun, Yongliang Zhang, Yaohua Representation Theory Rings and Algebras In this paper, we establish a dual framework for Neeman's results concerning triangulated categories with compact silting objects by employing Brown--Comenetz duality. This framework introduces an intrinsic non-compact subcategory, provides its characterization, and demonstrates representability theorems for both the low-bounded and bounded subcategories. Additionally, it elucidates how recollements are restricted to short exact sequences on the dual (non-compact) side. Several localization results and specific applications are also derived. |
| title | Triangulated categories with a compact silting object, Brown-Comenetz duality and Brown representability theorems |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2602.14383 |