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On non-commutative twisting in étale and motivic cohomology

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Hornbostel, Jens ; Kings, Guido
Date of publication of this fulltext: 12 Apr 2010 05:45


It is proved that under a technical condition the ¶etale cohomol-
ogy groups H1(OK[1=S];Hi(¹X ;Qp(j)), where X SpecOK[1=S] is
a smooth, projective scheme, are generated by twists of norm com-
patible units in a tower of number ¯elds associated to Hi(¹X; Zp(j)).
This con¯rms a consequence of the non-abelian Iwasawa main conjec-
ture. Using the \Bloch-Kato-conjecture" a similar result is proven for
motivic cohomology with ¯nite coe±cients.

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