The Chevalley–Gras formula over global fields
Journal de Théorie des Nombres de Bordeaux, Volume 32 (2020) no. 2, pp. 525-543.

In this article we give an adelic proof of the Chevalley–Gras formula for global fields, which itself is a generalization of the ambiguous class number formula. The idea is to reduce the formula to the Hasse norm theorem and to the local and global reciprocity laws. We also give an adelic proof of the Chevalley–Gras formula for the class group of divisors of degree 0 in the function field case, which extends a result of Rosen.

Dans cet article, nous donnons une preuve adélique de la formule de Chevalley–Gras pour les corps de nombres qui, elle-même, est une généralisation de la formule du nombre de classes ambiges. L’idée est de réduire cette formule au théorème de la norme de Hasse et à des lois de réciprocité globaux. Nous donnons également une preuve adélique de la formule de Chevalley–Gras pour les groupes des classes des diviseurs de degré 0 dans le cas des corps de fonctions, qui étend un résultat de Rosen.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1133
Classification: 11R29,  11R37,  11R34
Keywords: class groups, ambiguous class number formulas, class field theory
Jianing Li 1; Chia-Fu Yu 2

1 CAS Wu Wen-Tsun Key Laboratory of Mathematics University of Science and Technology of China Hefei, Anhui 230026, China
2 Institute of Mathematics, Academia Sinica and NCTS Astronomy Mathematics Building No. 1, Roosevelt Rd. Sec. 4 Taipei, 10617, Taiwan
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Jianing Li; Chia-Fu Yu. The Chevalley–Gras formula over global fields. Journal de Théorie des Nombres de Bordeaux, Volume 32 (2020) no. 2, pp. 525-543. doi : 10.5802/jtnb.1133. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1133/

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