[Sur le genre dʼun corps gauche]
Nous définissons le genre dʼun corps gauche central D de dimension finie sur un corps K comme lʼensemble des classes dans le groupe de Brauer qui sont représentées par des corps gauches de centre K ayant les mêmes sous-corps maximaux que D. Nous donnons des exemples où est réduit à un seul élément, ainsi que dʼautres où est fini.
We define the genus of a finite-dimensional central division algebra D over a field K as the set of all classes in the Brauer group that are represented by central division K-algebras having the same maximal subfields as D. We give examples where is reduced to a single element, and other examples where it is finite.
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@article{CRMATH_2012__350_17-18_807_0,
author = {Chernousov, Vladimir I. and Rapinchuk, Andrei S. and Rapinchuk, Igor A.},
title = {On the genus of a division algebra},
journal = {Comptes Rendus. Math\'ematique},
pages = {807--812},
publisher = {Elsevier},
volume = {350},
number = {17-18},
year = {2012},
doi = {10.1016/j.crma.2012.09.014},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.09.014/}
}
TY - JOUR AU - Chernousov, Vladimir I. AU - Rapinchuk, Andrei S. AU - Rapinchuk, Igor A. TI - On the genus of a division algebra JO - Comptes Rendus. Mathématique PY - 2012 SP - 807 EP - 812 VL - 350 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.09.014/ DO - 10.1016/j.crma.2012.09.014 LA - en ID - CRMATH_2012__350_17-18_807_0 ER -
%0 Journal Article %A Chernousov, Vladimir I. %A Rapinchuk, Andrei S. %A Rapinchuk, Igor A. %T On the genus of a division algebra %J Comptes Rendus. Mathématique %D 2012 %P 807-812 %V 350 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.09.014/ %R 10.1016/j.crma.2012.09.014 %G en %F CRMATH_2012__350_17-18_807_0
Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. On the genus of a division algebra. Comptes Rendus. Mathématique, Tome 350 (2012) no. 17-18, pp. 807-812. doi : 10.1016/j.crma.2012.09.014. http://www.numdam.org/articles/10.1016/j.crma.2012.09.014/
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