Réalisations des complexes motiviques de Voevodsky

Florence Lecomte (1) , Nathalie Wach (1)

1 IRMA - Institut de Recherche Mathématique Avancée

Over a number field k, we construct realizations of Voevodsky motivic complexes, realizations as presented by Fontaine and Perrin-Riou [FPR94]. Our realization functors are defined from the category of motivic complexes constructed by Voevodsky and are obtained as cohomological functors which are, up to some limits, representable. The De Rham realization is represented by the De Rham motivic complex defined in [LW09]. We obtain integral Betti and l-adic realizations. Our realization functors are related by comparison arrows, which become isomorphisms when restricted to the category of geometrical motives. Furthermore, on geometrical motives, the realizations are endowed with Bondarko's weight filtration [Bo09], the Hodge realization is constructed and all these realizations coincide rationally with those defined by A. Huber [H00].

Mots clés: motifs : réalisations

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]; K-théorie et homologie [math.KT]

Florence Lecomte, Nathalie Wach. Réalisations des complexes motiviques de Voevodsky. 2009. ⟨hal-00437302v2⟩