The projectors of the decomposition theorem are motivic

2014/01/15 by Mark Andrea A. de Cataldo, de Cataldo, Mark Andrea A., Luca Migliorini +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1401.3705

arxiv created 2014/01/15 · arxiv updated 2014/01/16

Abstract

We prove that the projectors arising from the decomposition theorem applied to a projective map of quasi projective varieties are absolute Hodge, André motivated, Tate and Ogus classes. As a by-product, we introduce, in characteristic zero, the notions of algebraic de Rham intersection cohomology groups of a quasi projective variety and of intersection cohomology motive of a projective variety.

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