Résumé:
"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."