Unbounded ladders induced by Gorenstein algebras

Abstract

The derived category $D(\mathrm{Mod}A)$ of a Gorenstein triangular matrix algebra $A$ admits an unbounded ladder; and this ladder restricts to $D^{-}(\mathrm{Mod})$ {\rm(}resp. $D^b(\mathrm{Mod})$, $D^b(\mathrm{mod})$, $K^b(\mathrm{proj})${\rm)}. A left recollement of triangulated categories with Serre functors sits in a ladder of period $1$; as an application, the singularity category of $A$ admits a ladder of period $1$.

11 pages