English

The correspondence between silting objects and $t$-structures for non-positive dg algebras

Representation Theory 2024-12-30 v3

Abstract

We establish a bijective correspondence between isomorphism classes of basic silting objects of per(A)\mathsf{per}(A) and algebraic tt-structures of Dfd(A)\mathsf{D}_{\rm fd}(A) for locally finite non-positive dg algebra AA over a field kk (more generally, we work in the setting of ST-pair inside an algebraic triangulated category). For a non-positive (topologically) homologically smooth dg kk-algebra AA whose zeroth cohomology is finite-dimensional, or for a non-positive proper dg kk-algebra AA, the one-to-one correspondence between isomorphism classes of basic silting objects of per(A)\mathsf{per}(A) and algebraic tt-structures on Dfd(A)\mathsf{D}_{\rm fd}(A) was already known. The main result of this paper generalizes the above two results to locally finite non-positive dg kk-algebras.

Keywords

Cite

@article{arxiv.2312.17597,
  title  = {The correspondence between silting objects and $t$-structures for non-positive dg algebras},
  author = {Riku Fushimi},
  journal= {arXiv preprint arXiv:2312.17597},
  year   = {2024}
}

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13 pages