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Comptes Rendus Mathématique
Volume 337, n° 1
pages 1-6 (juillet 2003)
Doi : 10.1016/S1631-073X(03)00261-9
Received : 7 December 2002 ;  accepted : 20 May 2003
Le groupe   d'une algèbre de biquaternions
The group   of a biquaternion algebra

Baptiste  Calmès
Équipe de topologie et géométrie algébriques, Université Paris 7, 175, rue du Chevaleret, 75013 Paris, France 

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L'objet de cette Note est de décrire les grandes lignes de la démonstration de l'exactitude d'une suite qui relie le groupe   (noyau de la norme réduite) d'une algèbre de biquaternions sur un corps   au groupe de cohomologie galoisienne  . Cette suite est obtenue en utilisant certaines suites spectrales en cohomologie motivique ainsi que le calcul d'une partie de la filtration topologique d'une quadrique d'Albert. Pour citer cet article : B. Calmès, C. R. Acad. Sci. Paris, Ser. I 337 (2003).

Abstract

In this Note, I will sketch the proof that a sequence relating the group   (kernel of the reduced norm) of a biquaternion algebra over a field   and the Galois cohomology group   is exact. The main steps of the proof contain computations in spectral sequences for motivic cohomology and in the topological filtration of an Albert quadric. To cite this article: B. Calmès, C. R. Acad. Sci. Paris, Ser. I 337 (2003).




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