The Leray spectral sequence is motivic
Abstract
Our goal is to prove that the Leray spectral sequence associated to a map of algebraic varieties is motivic in the following sense: If the singular cohomology groups of the category of quasiprojective varieties defined over a subfield of C can be canonically endowed with some additional structure, such as its mixed Hodge structure or its motive (in Nori's sense or as a product of realizations). Then the Leray spectral sequence for a projective map in this category is automatically compatible with this structure. As byproduct, we get a relatively cheap construction of a mixed Hodge structure on the cohomology of variation of Hodge structure of geometric origin.
Keywords
Cite
@article{arxiv.math/0301140,
title = {The Leray spectral sequence is motivic},
author = {Donu Arapura},
journal= {arXiv preprint arXiv:math/0301140},
year = {2009}
}
Comments
19 pages, latex, uses xypic, contain eps graphics; Final Revision (to appear in Invent. Math.)