On non-commutative twisting in étale and motivic cohomology
Annales de l'Institut Fourier, Volume 56 (2006) no. 4, p. 1257-1279

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.

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.

DOI : https://doi.org/10.5802/aif.2212
Classification:  11R23,  14G40,  14F42,  11R32
Keywords: Étale cohomology, motivic cohomology, non-commutative Iwasawa-theory
@article{AIF_2006__56_4_1257_0,
     author = {Hornbostel, Jens and Kings, Guido},
     title = {On non-commutative twisting in \'etale and motivic cohomology},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {56},
     number = {4},
     year = {2006},
     pages = {1257-1279},
     doi = {10.5802/aif.2212},
     mrnumber = {2266890},
     zbl = {pre05145722},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2006__56_4_1257_0}
}
Hornbostel, Jens; Kings, Guido. On non-commutative twisting in étale and motivic cohomology. Annales de l'Institut Fourier, Volume 56 (2006) no. 4, pp. 1257-1279. doi : 10.5802/aif.2212. http://www.numdam.org/item/AIF_2006__56_4_1257_0/

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