In this paper, we construct realizations of motivic complexes over a number field. The De Rham realization is represented by a motivic De Rham complex and has a Hodge filtration. The Betti and l-adic realizations are integrally defined. When restricted to geometrical motives, the realization functors are endowed with Bondarko's weight filtration and rationally agree with Huber's realizations.
Florence Lecomte <firstname.lastname@example.org>
Nathalie Wach <email@example.com>