Réalisation l-adique des motifs triangulés géométriques, by Florian Ivorra

In the first part of this work, we provide an integral l-adic realization functor for Voevodsky's triangulated category of geometrical motives over a noetherian separated scheme. Our approach to the realization problem is to study finite correspondences from the Nisnevich and étale local point of view. We set the existence of a local decomposition for finite correspondences which allows us to carry out the construction of the l-adic realization functor. We also give a moderate l-adic realization in some geometrical situations. For geometrical triangulated motives with rational coefficients over a ground field of characteristic zero which is embeddable into C, A. Huber has constructed a realization functor with values in the category of mixed realization. In the second part of this work, we prove that the l-adic realization functor obtained in the first part is the same up to a canonical isomorphism than the l-adic component of A. Huber's construction. We also prove a comparison theorem with the classical l-adic cycle class map over a perfect field using an naive motivic cycle class map.

Florian Ivorra <fivorra@math.jussieu.fr>