On weights for relative motives with integral coefficients

Abstract

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.

Several minor corrections (mostly in section 1.3) were made. arXiv admin note: substantial text overlap with arXiv:1007.4543

References in corpus (1)

• Gersten weight structures for motivic homotopy categories; direct summands of cohomology of function fields and coniveau spectral sequences

Cited by in corpus (2)

• Étale motives
• Gersten weight structures for motivic homotopy categories; direct summands of cohomology of function fields and coniveau spectral sequences