On non-commutative twisting in étale and motivic cohomology
[Sur la torsion non commutative en cohomologie étale et motivique]
Annales de l'Institut Fourier, Tome 56 (2006) no. 4, pp. 1257-1279.

Cet article confirme une conséquence de la conjecture principale de la théorie d’Iwasawa non abélienne. On démontre que, sous une condition technique, les groupes de cohomologie étale H 1 (𝒪 K [1/S],H i (X ¯, p (j))), où XSpec𝒪 K [1/S] est un schéma projectif lisse, sont engendrés par des unités tordues compatible par rapport aux normes dans une tour de corps de nombres associés à H i (X ¯, p (j)). On établit un résultat similaire pour la cohomologie motivique à coefficients finis en utilisant la conjecture de Bloch-Kato.

This article confirms a consequence of the non-abelian Iwasawa main conjecture. It is proved that under a technical condition the étale cohomology groups H 1 (𝒪 K [1/S],H i (X ¯, p (j))), where XSpec𝒪 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 ¯, p (j)). Using the “Bloch-Kato-conjecture” a similar result is proven for motivic cohomology with finite coefficients.

DOI : 10.5802/aif.2212
Classification : 11R23, 14G40, 14F42, 11R32
Keywords: Étale cohomology, motivic cohomology, non-commutative Iwasawa-theory
Mot clés : cohomologie étale, cohomologie motivique, théorie d’Iwasawa non-commutative
Hornbostel, Jens 1 ; Kings, Guido 

1 Universität Regensburg NWF I, Mathematik 93040 Regensburg (Germany)
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Hornbostel, Jens; Kings, Guido. On non-commutative twisting in étale and motivic cohomology. Annales de l'Institut Fourier, Tome 56 (2006) no. 4, pp. 1257-1279. doi : 10.5802/aif.2212. http://www.numdam.org/articles/10.5802/aif.2212/

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