On motivic cohomology with $\mathbf{Z}/l$-coefficients


In this paper we prove the conjecture of Bloch and Kato which relates Milnor’s $K$-theory of a field with its Galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the Nisnevich and étale topologies.


Vladimir Voevodsky

School of Mathematics
Institute for Advanced Study
Einstein Drive
Princeton, NJ 08540