Motifs génériques, by Frédéric Déglise

In this paper, we introduce certain type of pro-object in the triangulated category geometric mixed motives defined by V. Voevodsky. These pro-motives are attached to a finite type extension of the base field and to an integer and are called generic motives (with weight).

Especially, we show that these generic motives are subject to a functoriality which is dictated by the axioms of a cycle pre-module as defined by M. Rost. This involves in particular a study of the functoriality of triangulated mixed motives such as the functoriality of the Gysin triangle.

These results show in particular that any cohomology which induces a realisation functor from the category of triangulated mixed motives defines canonically a cycle module.

[ preprint updated Jan 13, 2006, replacing one dated May 7, 2004. ]

Frédéric Déglise <>