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.
Classification : 11R52, 11E41, 11R56, 11R37, 16G30.
Mots clés : norme spinorielle, genre spinoriel, champs de classe, formes anti-hermitiennes, ordres maximaux, algèbres simples centrales
@article{AIF_2003__53_7_2021_0, author = {Arenas-Carmona, Luis}, title = {Applications of spinor class fields: embeddings of orders and quaternionic lattices}, journal = {Annales de l'Institut Fourier}, pages = {2021--2038}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {7}, year = {2003}, doi = {10.5802/aif.1999}, zbl = {1060.11018}, mrnumber = {2044166}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1999/} }
TY - JOUR AU - Arenas-Carmona, Luis TI - Applications of spinor class fields: embeddings of orders and quaternionic lattices JO - Annales de l'Institut Fourier PY - 2003 DA - 2003/// SP - 2021 EP - 2038 VL - 53 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1999/ UR - https://zbmath.org/?q=an%3A1060.11018 UR - https://www.ams.org/mathscinet-getitem?mr=2044166 UR - https://doi.org/10.5802/aif.1999 DO - 10.5802/aif.1999 LA - en ID - AIF_2003__53_7_2021_0 ER -
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. http://www.numdam.org/articles/10.5802/aif.1999/
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