The Milnor Conjecture, by Vladimir Voevodsky

In this paper we prove that for any field of characteristic not equal to 2 the norm residue homomorphism with Z/2-coefficients is an isomorphism in all dimensions. As an application we deduce a number of results about motivic cohomology, etale cohomology and algebraic K-theory with Z/2-coefficients. The applications to the theory of quadratic forms will be considered in a separate paper.

Vladimir Voevodsky <>