Triangulated categories of mixed motives

Overview & Synopsis

We construct triangulated categories of mixed motives over a noetherian scheme of finite dimension, extending Voevodsky's definition of motives over a field. We prove that motives with rational coefficients satisfy the formalism of the six operations of Grothendieck. This includes the analog of the absolute purity theorem and the stability of constructibility under the six operations known for l-adic sheaves. Finally, we associate to any mixed Weil cohomology a system of categories of coefficients and well behaved realization functors.