Descent, Motives and K-theory

In this paper we show how to write any variety over a field of characteristic zero as the difference of two pure motives, thus answering a question asked by Serre (in arbitrary characteristic, [Se] p.341). The Grothendieck theory of (pure effective Chow) motives starts with the category V of smooth projective varieties over a field k. A motive is a pair (X… CONTINUE READING