Titre: Localized category of differential complexes

L. Fiorot

"The category of differential complexes natural appears as a "good" category where the De Rham functor takes image. We are interested in finding a category, purely algebraic defined, where the De Rham functor takes image and where we can develop the formalism of six Grothendieck operations. Two possible candidates are the category of differential complexes introduced by Herrera-Liebermann, opportunely localized (called Db1(OX,Diff)), and that of Morihiko Saito (called Db(OX,Diff)). Saito choice is very interesting because his category is equivalent, via the functor DR and DR-1, to the bounded derived category of D-Modules; however the formalism of Grothendieck operations is only partial in fact, for example, there is no definition of the functor f*; while in the Herrera-Liebermann category the Grothendieck operations are easier. We prove that these localized categories of differential complexes are equivalent."