Réalisations de Hodge des motifs de Voevodsky

Florence Lecomte (1) , Nathalie Wach (1)

1 IRMA - Institut de Recherche Mathématique Avancée

Over a subfield of the field of complex numbers, the Hodge realization of a geometrical motive is defined and represented as the cohomology of a mixed Hodge DG-complex in the sense of Deligne. Both filtrations are represented by truncation functors, on a Bondarko weight complex for the weight filtration and on the De Rham motivic complex for the Hodge one. The Deligne-Beilinson realization is also constructed. This preprint partially replaces the former "Réalisation des complexes motiviques de Voevodsky".

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 de Hodge des motifs de Voevodsky. Manuscripta mathematica, 2013, 141, pp.663-697. ⟨10.1007/s00229-012-0587-5⟩. ⟨hal-00437302v3⟩