Fishing for complements
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910246892470272 |
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| author | Hügel, Lidia Angeleri Pauksztello, David Vitória, Jorge |
| author_facet | Hügel, Lidia Angeleri Pauksztello, David Vitória, Jorge |
| contents | Given a presilting object in a triangulated category, we find necessary and sufficient conditions for the existence of a complement. This is done both for classic (pre)silting objects and for large (pre)silting objects. The key technique is the study of associated co-t-structures. As a consequence of our techniques we recover some known cases of the existence of complements, including for derived categories of some hereditary abelian categories and for silting-discrete algebras. Moreover, we also show that a finite-dimensional algebra is silting discrete if and only if every bounded large silting complex is equivalent to a compact one. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_13356 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fishing for complements Hügel, Lidia Angeleri Pauksztello, David Vitória, Jorge Representation Theory Rings and Algebras 18G05, 18G80, 16G10 Given a presilting object in a triangulated category, we find necessary and sufficient conditions for the existence of a complement. This is done both for classic (pre)silting objects and for large (pre)silting objects. The key technique is the study of associated co-t-structures. As a consequence of our techniques we recover some known cases of the existence of complements, including for derived categories of some hereditary abelian categories and for silting-discrete algebras. Moreover, we also show that a finite-dimensional algebra is silting discrete if and only if every bounded large silting complex is equivalent to a compact one. |
| title | Fishing for complements |
| topic | Representation Theory Rings and Algebras 18G05, 18G80, 16G10 |
| url | https://arxiv.org/abs/2402.13356 |