Bloch-Kato conjecture and motivic cohomology with finite coefficients, by A. Suslin and V. Voevodsky

In this paper we prove the equivalence of two well known conjectures - the Bloch-Kato conjecture which asserts that the cotorsion in Milnor's K-groups of a field is isomorphic to its etale cohomology and the Beilinson-Lichtenbaum conjecture which provides a complete description of the motivic cohomology with finite coefficients in terms of the etale cohomology. Since the Bloch-Kato conjecture is known in dimension 2 (and in dimension 3 for Z/2-coefficients) we obtain in particular a proof of the Beilinson-Lichtenbaum conjecture in weight 2 and in weight 3 for Z/2-coefficients.

A. Suslin <>
V. Voevodsky <>