We define a theory of étale motives over a noetherian scheme. This provides a system of
categories of complexes of motivic sheaves with integral coefficients which is closed under …

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 …

We recall the construction, following the method of Morel and Voevodsky, of the triangulated
category of étale motivic sheaves over a base scheme. We go through the formalism of …

−(k) which is called the triangulated category of (effective) motivic complexes over k (the
minus sign indicates that we consider only complexes bounded from the above). This …

Provides an account of the triangulated theory of motives. The book's purpose is to introduce
Motivic Cohomology, to develop its main properties, and finally to relate it to other known …

Triangulated categories of motives 189 complexes over k (the minus sign indicates that we
consider only complexes bounded from the above). This construction provides a natural …

We describe explicitly the Voevodsky's triangulated category of motives (and give a
'differential graded enhancement'of it). This enables us to able to verify that DMgm ℚ is (anti) …

The theory of motives has always had two faces. One is the geometric face where a
universal cohomology theory for varieties is cooked up from geometric objects like cycles …

We start developing a notion of reciprocity sheaves, generalizing Voevodsky's homotopy
invariant presheaves with transfers which were used in the construction of his triangulated …

For noetherian schemes of finite dimension over a field of characteristic exponent p, we
study the triangulated categories of Z [1/p]-linear mixed motives obtained from cdh-sheaves …