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.

Reçu le : 2005-01-06
Accepté le : 2005-09-09
DOI : https://doi.org/10.5802/aif.2212
Classification : 11R23,  14G40,  14F42,  11R32
Mots clés: cohomologie étale, cohomologie motivique, théorie d’Iwasawa non-commutative
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     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},
     zbl = {pre05145722},
     mrnumber = {2266890},
     language = {en},
     url = {aif.centre-mersenne.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, Tome 56 (2006) no. 4, pp. 1257-1279. doi : 10.5802/aif.2212. https://aif.centre-mersenne.org/item/AIF_2006__56_4_1257_0/

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