K-Cohomology of severi-brauer varieties and the norm residue homomorphism

The basic purpose of this paper is to prove bijectivity of the norm residue homomorphism for any field of characteristic prime to. In particular, if, then any central simple algebra of exponent is similar to a tensor product of cyclic algebras. In the course of the proof we obtain partial degeneracy of the Gersten spectral sequence, and we compute some -cohomology groups of Severi-Brauer groups corresponding to cyclic algebras of prime degree. The fundamental theorem also gives us several corollaries.Bibliography: 27 titles.