Representation fields for commutative orders
Annales de l'Institut Fourier, Volume 62 (2012) no. 2, pp. 807-819.

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.

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 F et nous donnons une formule pour F. Le résultat principal est prouvé pour des algèbres simples centrales sur des corps globaux arbitraires.

DOI: 10.5802/aif.2695
Classification: 11R52, 11R56, 11R37, 16G30, 16G10
Keywords: maximal orders, central simple algebras, spinor genera, spinor class fields
Mot clés : ordres maximaux, algèbres centrales simples, genre spinoriel, corps de classes spinoriel
Arenas-Carmona, Luis 1

1 Universidad de Chile Departamento de matematicas Facultad de ciencia Casilla 653 Santiago (Chile)
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Arenas-Carmona, Luis. Representation fields for commutative orders. Annales de l'Institut Fourier, Volume 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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