Mathematical Research Letters

Volume 22 (2015)

Number 4

The projectors of the decomposition theorem are motivated

Pages: 1061 – 1088



Mark Andrea de Cataldo (Department of Mathematics, Stony Brook University, Stony Brook, New York, U.S.A.)

Luca Migliorini (Dipartimento di Matematica, Università di Bologna, Italy)


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 quasiprojective variety and of intersection cohomology motive of a projective variety.

Published 24 July 2015