The Leray spectral sequence is motivic

Details The Leray spectral sequence is motivic The Leray spectral sequence is motivic

2003-01-13

arxiv.org/abs/math/0301140v3

Mathematics

Algebraic Geometry

19 pages, latex, uses xypic, contain eps graphics; Final Revision (to appear in Invent. Math.)

Scientific paper

10.1007/s00222-004-0416-x

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.

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