[Corps de representations pour ordres commutatifs]
Un corps de représentation pour un ordre non maximal dans une algèbre centrale simple est un sous-corps du corps de classes spinoriel d’ordres maximaux qui détermine l’ensemble de genres spinoriels d’ordres maximaux qui contiennent un conjugué de . Un ordre non maximal ne possède pas forcément un corps de représentation. Dans ce travail, nous montrons que chaque ordre commutatif a un corps de représentation et nous donnons une formule pour . Le résultat principal est prouvé pour des algèbres simples centrales sur des corps globaux arbitraires.
A representation field for a non-maximal order in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of . Not every non-maximal order has a representation field. In this work we prove that every commutative order has a representation field and give a formula for it. The main result is proved for central simple algebras over arbitrary global fields.
Classification : 11R52, 11R56, 11R37, 16G30, 16G10
Mots clés : ordres maximaux, algèbres centrales simples, genre spinoriel, corps de classes spinoriel
@article{AIF_2012__62_2_807_0,
author = {Arenas-Carmona, Luis},
title = {Representation fields for commutative orders},
journal = {Annales de l'Institut Fourier},
pages = {807--819},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {62},
number = {2},
year = {2012},
doi = {10.5802/aif.2695},
mrnumber = {2985517},
zbl = {1269.11115},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2695/}
}
TY - JOUR AU - Arenas-Carmona, Luis TI - Representation fields for commutative orders JO - Annales de l'Institut Fourier PY - 2012 DA - 2012/// SP - 807 EP - 819 VL - 62 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2695/ UR - https://www.ams.org/mathscinet-getitem?mr=2985517 UR - https://zbmath.org/?q=an%3A1269.11115 UR - https://doi.org/10.5802/aif.2695 DO - 10.5802/aif.2695 LA - en ID - AIF_2012__62_2_807_0 ER -
Arenas-Carmona, Luis. Representation fields for commutative orders. Annales de l'Institut Fourier, Tome 62 (2012) no. 2, pp. 807-819. doi : 10.5802/aif.2695. http://www.numdam.org/articles/10.5802/aif.2695/
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