English

Recollements induced by good silting objects

Category Theory 2019-12-09 v2

Abstract

Let UU be a silting object in a derived category over a dg-algebra AA, and let BB be the endomorphism dg-algebra of UU. Under some appropriate hypotheses, we show that if UU is good, then there exist a dg-algebra CC, a homological epimorphism BCB\rightarrow C and a recollement among the (unbounded) derived categories D(C,d)\mathbf{D}(C,d) of CC, D(B,d)\mathbf{D}(B,d) of BB and D(A,d)\mathbf{D}(A,d) of AA. In particular, the kernel of the left derived functor BLU-\otimes^{\mathbb{L}}_{B}U is triangle equivalent to the derived category D(C,d)\mathbf{D}(C,d). Conversely, if BLU-\otimes^{\mathbb{L}}_{B}U admits a fully faithful left adjoint functor, then UU 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.

Keywords

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

R2 v1 2026-06-23T12:35:54.127Z