On derived categories of differential complexes

This paper is devoted to the comparison of different localized categories of differential complexes. The main result is an explicit equivalence between the category of differential complexes of order one (defined by Herrera and Lieberman) and the category of differential complexes (of any order, defined by M. Saito), both localized with respect to a suitable notion of quasi-isomorphism. Then we prove a similar result for a filtered version of the previous categories (defined respectively by Du Bois and M. Saito), localized with respect to graded-quasi-isomorphisms, thus answering a question posed by M. Saito.