Séminaire de Géométrie Algébrique de Rennes - Exposé du 25 septembre 2003


Luisa FIOROT (Padova)


Titre : Localized category of differential complexes

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 $D^b_1(O_X,Diff)$), and that of Morihiko Saito (called $D^b(O_X,Diff)$). 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.