Triangulated categories of motives over a field, by Vladimir Voevodsky

In this paper we define and study the triangulated category of mixed motives over a field. At least in the case when there is resolution of singularities, we are able to prove that this category is has a natural duality and that the Hom-groups between Tate objects are canonically isomorphic to the corresponding higher Chow groups. A detailed of summary of results of the paper is given in the first section.

This replaces an earlier version.

Vladimir Voevodsky <>