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On non-commutative twisting in etale and motivic cohomology

J. Hornbostel·G. Kings
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Abstract

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 V_p(j) for large Tate-twist j and V_p a Q_p vector space. We show that under a technical hypothesis that H^1(K, V_p(j)) is generated by twists of norm-compatible units in an infinite tower of number fields with elements in V_p(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.

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J. Hornbostel, G. Kings. 2004-04-15. On non-commutative twisting in etale and motivic cohomology. https://arxiv.org/abs/math/0404263

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