Norm Varieties, by Andrei Suslin and Seva Joukhovitski

For a given symbol in the n-th Milnor K-group modulo prime l we construct a splitting variety with several properties. This variety is l-generic, meaning that it is generic with respect to splitting fields having no finite extensions of degree prime to l. The degree of its top Milnor class is not divisible by l2 and a certain motivic cohomology group of this variety consists of units. The existence of such varieties is needed in Voevodsky's part of the proof of the Bloch-Kato conjecture. In the course of the proof we also establish Markus Rost's degree formula.

Note: This paper is to appear in the Journal of Pure and Applied Algebra.

[ Updated version provided January 30, 2006, to replace original version dated May 13, 2005. ]

Andrei Suslin <>
Seva Joukhovitski <>