On non-commutative twisting in etale and motivic cohomology

الأصل · EN

In this paper we use ideas of the non-abelian Iwasawa main conjecture to prove a result about the first Galois cohomology of continuous Galois modules Vₚ(j) for large Tate-twist j and Vₚ a Qₚ vector space. We show that under a technical hypothesis that H¹(K, Vₚ(j)) is generated by twists of norm-compatible units in an infinite tower of number fields with elements in Vₚ(j-1). This confirms a consequence of the non-abelian Iwasawa main conjecture. Using the "Bloch-Kato-conjecture" a similar result is proven for motivic cohomology with finite coefficients.