The projectors of the decomposition theorem are motivic

TL;DR

This paper demonstrates that projectors from the decomposition theorem are motivic and absolute Hodge classes, introducing algebraic de Rham intersection cohomology and intersection cohomology motives in characteristic zero.

Contribution

It establishes the motivic nature of projectors from the decomposition theorem and introduces new concepts of algebraic de Rham intersection cohomology and intersection cohomology motives.

Findings

Projectors are shown to be absolute Hodge, motivated, Tate, and Ogus classes.

Introduces algebraic de Rham intersection cohomology groups.

Defines intersection cohomology motive for quasi projective varieties.

Abstract

We prove that the projectors arising from the decomposition theorem applied to a projective map of quasi projective varieties are absolute Hodge, Andr\'e 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.