Recollements induced by good silting objects
Abstract
Let be a silting object in a derived category over a dg-algebra , and let be the endomorphism dg-algebra of . Under some appropriate hypotheses, we show that if is good, then there exist a dg-algebra , a homological epimorphism and a recollement among the (unbounded) derived categories of , of and of . In particular, the kernel of the left derived functor is triangle equivalent to the derived category . Conversely, if admits a fully faithful left adjoint functor, then is good. Moreover, we establish a criterion for the existence of a recollement of the derived category of a dg-algebra relative to two derived categories of weak non-positive dg-algebras. Finally, some applications are given related to good cosilting objects, good 2-term silting complexes, good tilting complexes and modules, which recovers a recent result by Chen and Xi.
Cite
@article{arxiv.1912.02111,
title = {Recollements induced by good silting objects},
author = {Rongmin Zhu and Jiaqun Wei},
journal= {arXiv preprint arXiv:1912.02111},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1707.07353, arXiv:arXiv:1012.2176, arXiv:1705.10981 by other authors