Abstract
For any subfield k of the field of complex numbers C, we construct a Betti realization functor from the category DM − ( k ) of Voevodsky motivic complexes over k to the category of graded abelian groups. If X is a scheme of finite type over k, the image of the associated motive through this functor is the singular cohomology ⊕ p ⩾ 0 H p ( X ( C ) , Z ) of the variety X ( C ) of complex points. To cite this article: F. Lecomte, C. R. Acad. Sci. Paris, Ser. I 346 (2008).
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