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Perverse, Hodge and motivic realizations of étale motives

Published online by Cambridge University Press:  26 February 2016

Florian Ivorra*
Affiliation:
Institut de Recherche Mathématique de Rennes, UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France email florian.ivorra@univ-rennes1.fr
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Abstract

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Let $k=\mathbb{C}$ be the field of complex numbers. 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 $k$-scheme, the construction done by Nori over a field, and relies on the original version of the basic lemma proved by Beĭlinson. 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 motives.

Type
Research Article
Copyright
© The Author 2016 

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