### 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 *l*^{2} 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 <suslin@math.northwestern.edu>

Seva Joukhovitski <seva@math.ucla.edu>