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. ]