The Leray spectral sequence is motivic

By D. Arapura. 2003

77 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e3025990eba5a5ae9a1a5dd2c964be48bacd0ff9

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Hodge genera of algebraic varieties I (2006, background): “(3.2) i 0QX! f (QX) can ! f (QX) [ 1 ] !”
The structure of the tautological ring in genus one (2012, methodology): “ic varieties are compatible with the mixed Hodge structures, either by Saito’s theory (using the non-perverse t-structure on the derived category of mixed Hodge modules [Sai90, Remark 4.6.(2)]) or by [Ara05]. When the Cohen–Taylor sequence is written in the form we are using here, one needs to inclu”
Hodge polynomials of SL (2,C)-character varieties for curves of small genus (2013, methodology): “The result of [1] asserts its existence, and we use the functorial property for computing it.”