English

The ST correspondence for proper non-positive dg algebras

Representation Theory 2021-05-11 v1 Category Theory

Abstract

Let AA be a proper non-positive dg algebra over a field kk. For a simple-minded collection of the finite-dimensional derived category Dfd(A)\mathcal{D}_{fd}(A), we construct a 'dual' silting object of the perfect derived category per(A)\mathrm{per}(A) by using the Koszul duality for dg algebras. This induces a one-to-one correspondence between the equivalence classes of silting objects in per(A)\mathrm{per}(A) and algebraic t-structures of Dfd(A)\mathcal{D}_{fd}(A).

Keywords

Cite

@article{arxiv.2105.04095,
  title  = {The ST correspondence for proper non-positive dg algebras},
  author = {Houjun Zhang},
  journal= {arXiv preprint arXiv:2105.04095},
  year   = {2021}
}