the category of Chow motives over k. To every variety X over k one associates
a finite complex W(X) in M(k), called the weight complex
of X. As a consequence of this construction one
shows that the weight filtration of a complex variety makes sense for the Betti
cohomology with integral coefficients, and not only
Furthermore, if one neglects torsion, the weight complex
W(X) is defined for any variety X on an excellent Dedekind domain.