no. 7
Applications of spinor class fields: embeddings of orders and quaternionic lattices
[Applications des corps de classes spinoriels : plongements des ordres et réseaux quaternioniques]
Arenas-Carmona, Luis1
1 Universidad de Chile, Facultad de Ciencias, Casilla 653, Santiago (Chili)
Annales de l'Institut Fourier, Tome 53 (2003) no. 7, pp. 2021-2038.

Nous étendons la théorie des corps de classe spinoriels et corps de classes spinoriels relatifs à l'étude des problèmes de représentation des réseaux par rapport à plusieurs groupes algébriques linéaires classiques sur les corps de nombres. Nous appliquons cette théorie pour étudier l'ensemble des classes d'isomorphismes d'ordres maximaux dans une algèbre centrale simple qui contiennent un sous-ordre abélien donné. Nous étudions aussi les isométries injectives d'un réseau anti-hermitien quaternionique dans un autre.

We extend the theory of spinor class fields and relative spinor class fields to study representation problems in several classical linear algebraic groups over number fields. We apply this theory to study the set of isomorphism classes of maximal orders of central simple algebras containing a given maximal Abelian suborder. We also study isometric embeddings of one skew-Hermitian Quaternionic lattice into another.

DOI : 10.5802/aif.1999
Classification : 11R52, 11E41, 11R56, 11R37, 16G30.
Keywords: spinor norm, spinor genus, class fields, skew-Hermitian forms, maximal orders, central simple algebras
Mot clés : norme spinorielle, genre spinoriel, champs de classe, formes anti-hermitiennes, ordres maximaux, algèbres simples centrales

Arenas-Carmona, Luis 1

1 Universidad de Chile, Facultad de Ciencias, Casilla 653, Santiago (Chili) 
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Arenas-Carmona, Luis. Applications of spinor class fields: embeddings of orders and quaternionic lattices. Annales de l'Institut Fourier, Tome 53 (2003) no. 7, pp. 2021-2038. doi : 10.5802/aif.1999. https://aif.centre-mersenne.org/articles/10.5802/aif.1999/

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