A residue current associated with a twisting cochain: duality and comparison formula

Let ${\mathcal{F}}^{\bullet }$ be a complex of coherent ${\mathcal{O}}_X$-modules over a complex manifold $X$. We give a construction of a residue current associated with this complex that generalizes Andersson and Wulcan’s construction of a residue current associated with a coherent ${\mathcal{O}}_X$-module $\mathcal{F}$. The main ingredients are to give a construction of a residue current associated with a twisting cochain in the sense of Toledo and Tong and to establish a comparison formula for these currents that generalizes an analogous formula given by Lärkäng.