Comptes Rendus
no. 17-18
Algebra
On the genus of a division algebra
[Sur le genre dʼun corps gauche]

Présenté par : Jean-Pierre Serre

Vladimir I. Chernousov1 ; Andrei S. Rapinchuk2 ; Igor A. Rapinchuk3
1 Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
2 Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA
3 Department of Mathematics, Yale University, New Haven, CT 06520-8283, USA
Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 807-812.

Nous définissons le genre gen(D) dʼun corps gauche central D de dimension finie sur un corps K comme lʼensemble des classes [D′] dans le groupe de Brauer Br(K) qui sont représentées par des corps gauches D′ de centre K ayant les mêmes sous-corps maximaux que D. Nous donnons des exemples où gen(D) est réduit à un seul élément, ainsi que dʼautres où gen(D) est fini.

We define the genus gen(D) of a finite-dimensional central division algebra D over a field K as the set of all classes [D′] in the Brauer group Br(K) that are represented by central division K-algebras D′ having the same maximal subfields as D. We give examples where gen(D) is reduced to a single element, and other examples where it is finite.

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DOI : 10.1016/j.crma.2012.09.014
Vladimir I. Chernousov 1 ; Andrei S. Rapinchuk 2 ; Igor A. Rapinchuk 3

1 Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
2 Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA
3 Department of Mathematics, Yale University, New Haven, CT 06520-8283, USA 
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     title = {On the genus of a division algebra},
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     pages = {807--812},
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Vladimir I. Chernousov; Andrei S. Rapinchuk; Igor A. Rapinchuk. On the genus of a division algebra. Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 807-812. doi : 10.1016/j.crma.2012.09.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.09.014/

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