Motifs Génériques

Abstract

The aim of the article is to show that every mixed triangulated motive in the sense of V. Voevodsky determines a canonical cycle module in the sense of M. Rost. Our method consists of interpreting geometrically the axioms of cycle modules in a category of pro-motives called "generic motives". It is general enough to show at the same time that every cohomological theory which induces a realization of triangulated mixed motives defines a canonical cycle module. This is in particular applicable to De Rham and rigid cohomology.