Extensions de la filtration de Saito

We extend Saito's filtration to the Chow groups of a representable morphism of presheaves on Sch_C${\mathit{Sch}}_{\mathbb{C}}$, the category of schemes over C$\mathbb{C}$. Moreover, for a presheaf on the category of smooth and projective schemes over C$\mathbb{C}$, we define its higher Chow groups along with their filtrations.