Existence of Algebraic Hecke Characters
نویسندگان
چکیده
In this note, we will characterize a weak version of the Brumer-Stark conjecture in terms of existence of certain algebraic Hecke characters, which can be viewed as a generalization of Weil’s well-known Jacobi characters. As an application, we show that the Brumer-Stark conjecture in CM extensions implies the Brumer-Stark conjecture in general. Résumé: Dans cette note nous étudions l’équivalence d’une version affaiblie de la conjecture de Brumer-Stark et de l’existence de certains caractères algèbriques de Hecke, qui peuvent être considérés comme une généralisation des caractères de Jacobi bien connus. Comme application, nous montrons que la conjecture de Brumer-Stark pour les extensions CM entraine la conjecture de Brumer-Stark générale. Abridged French version Soit k un corps de nombres totalement réel, et soit K une extension abelienne finie de k, totalement complexe et de groupe de Galois G = Gal(K/k). Soit S un ensemble fini de nombres premiers contenant tous les premiers infinis et les premiers ramifiés dans K. Let
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