### Motives over simplicial schemes, by Vladimir Voevodsky

In this paper we define the triangulated category of motives over a
simplicial scheme. The morphisms between the Tate objects in this category
compute the motivic cohomology of the underlying scheme. In the last section
we consider the special case of "embedded" simplicial schemes, which
correspond to the subsheaves of the constant sheaf and naturally appear in
the descent problems for motivic cohomology such as the Bloch-Kato
conjecture.

Vladimir Voevodsky <vladimir@ias.edu>