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Perverse, Hodge and motivic realizations of étale motives

Part of: Homological algebra (Co)homology theory

Published online by Cambridge University Press:  26 February 2016

Florian Ivorra
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 [email protected]
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Abstract

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.

Keywords

motivesperverse sheavesmixed Hodge moduleshomotopical algebra

MSC classification

Primary: 14F42: Motivic cohomology; motivic homotopy theory 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 18G55: Homotopical algebra
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 6 , June 2016 , pp. 1237 - 1285
Copyright
© The Author 2016 

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