Mikhail V. Bondarko
Published 2013-04-08, updated 2013-12-27Version 2
The goal of this paper is to define a certain Chow weight structure for the category of Voevodsky's motivic complexes with integral coefficients (as described by Cisinski and Deglise) over any excellent finite-dimensional separated scheme $S$. Our results are parallel to (though substantially weaker than) the corresponding 'rational coefficient' statements proved by D. Hebert and the author. As an immediate consequence of the existence of 'weights', we obtain certain (Chow)-weight spectral sequences and filtrations for any (co)homology of $S$-motives.
Comments: Several minor corrections (mostly in section 1.3) were made. arXiv admin note: substantial text overlap with arXiv:1007.4543
On Chow weight structures for $cdh$-motives with integral coefficients
Weights for relative motives; relation with mixed complexes of sheaves
Strict $\mathbb A^1$-invariance theorem with integral coefficients over fields
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