Réalisations des complexes motiviques de Voevodsky

Florence Lecomte (1) , Nathalie Wach (1)

1 IRMA - Institut de Recherche Mathématique Avancée

For a number field k, we construct realizations of Voevodsky motivic complexes as defined by Deligne [D89] or Fontaine and Perrin-Riou [FPR94]. Our realization functors are defined from the category of motivic complexes defined by Voevodsky and are obtained as cohomological functors which are, up to some limits, representable. Thus, using Bondarko's work [Bo09], we can endow them with weight filtrations. 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. When restricted to the category of rational geometrical motives, they coi ncide with those defined by 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-00437302v1⟩