On non-commutative twisting in étale and motivic cohomology

Zusammenfassung

This article confirms a consequence of the non-abelian I wasawa main conjecture. It is proved that under a technical condition the etale cohomology groups H-1(O-K[1/S],H-i((X) over bar ,Q(p)(j))), where X -> SpecO(K)[1/S] is a smooth, projective scheme, are generated by twists of norm compatible units in a tower of number fields associated to H-i((X) over bar, Z(p) (j)). Using the "Bloch-Kato-conjecture" a similar result is proven for motivic cohomology with finite coefficients.