Il résulte des généralités sur les formes quadratiques que la classe spinorielle de la trace intégrale d’un corps de nombres détermine la signature et le discriminant du corps. Dans cet article, nous définissons une famille de corps de nombres, qui contient, entre autres, tous les corps galoisiens de degré impair modérément ramifiés, pour lesquels la réciproque est vraie. Autrement dit, pour un corps de nombres de cette famille, on montre que la classe spinorielle de la trace intégrale ne contient pas d’informations sur autres que celles qui sont fournies par le discriminant et la signature.
It follows from generalities of quadratic forms that the spinor class of the integral trace of a number field determines the signature and the discriminant of the field. In this paper we define a family of number fields, that contains among others all odd degree Galois tame number fields, for which the converse is true. In other words, for a number field in such family we prove that the spinor class of the integral trace carries no more information about than the discriminant and the signature do.
Accepté le : 2020-08-10
Publié le : 2021-01-08
Classification : 11R04, 11S15
Mots clés : Arithmetic invariants, tame fields, arithmetic equivalence, trace forms.
@article{JTNB_2020__32_3_711_0,
author = {Guillermo Mantilla-Soler},
title = {An introduction to oddly tame number fields.},
journal = {Journal de Th\'eorie des Nombres de Bordeaux},
pages = {711--717},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {32},
number = {3},
year = {2020},
doi = {10.5802/jtnb.1140},
language = {en},
url = {https://jtnb.centre-mersenne.org/item/JTNB_2020__32_3_711_0/}
}
Guillermo Mantilla-Soler. An introduction to oddly tame number fields.. Journal de Théorie des Nombres de Bordeaux, Tome 32 (2020) no. 3, pp. 711-717. doi : 10.5802/jtnb.1140. https://jtnb.centre-mersenne.org/item/JTNB_2020__32_3_711_0/
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