Abstract: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.
| Comments: | 26 pages, 1 figure. Comments are welcome! Journal accepted version with numbering matching the published version |
| Subjects: | Representation Theory (math.RT); Rings and Algebras (math.RA) |
| MSC classes: | 18G05, 18G80, 16G10 |
| Cite as: | arXiv:2402.13356 [math.RT] |
| (or arXiv:2402.13356v2 [math.RT] for this version) | |
| https://doi.org/10.48550/arXiv.2402.13356 arXiv-issued DOI via DataCite |
|
| Journal reference: | Nagoya Math. J. 261 (2026) e5 |
| Related DOI: | https://doi.org/10.1017/nmj.2025.10070
DOI(s) linking to related resources |
From: David Pauksztello [view email]
[v1]
Tue, 20 Feb 2024 20:16:42 UTC (29 KB)
[v2]
Fri, 22 May 2026 11:20:59 UTC (30 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。