Perverse, Hodge and motivic realizations of étale motives

Florian Ivorra (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this article, we construct Hodge realization functors defined on the triangulated categories of étale motives with rational coefficients. Our construction extends, to every smooth quasi-projective variety, the construction done by M. Nori over a point and relies on the original version of the basic lemma proved by A. Beilinson. As in the case considered by Nori, the realization functor factors through the bounded derived category of a perverse version of the Abelian category of Nori.

Mots clés: Motives; Hodge theory; perverse sheaves

Domaines: Géométrie algébrique [math.AG]

Florian Ivorra. Perverse, Hodge and motivic realizations of étale motives. Compositio Mathematica, 2016, 152 (6), pp.1237-1285. ⟨10.1112/S0010437X15007812⟩. ⟨hal-00978894⟩