Let l be an odd prime number, F denote any totally real number field and E/F be an Abelian CM extension of F of conductor f. In this paper we prove that for every n odd and almost all prime numbers l we have where Sn(E/F,l) is the Stickelberger ideal (Ann. of Math. 135 (1992) 325–360; J. Coates, p-adic L-functions and Iwasawa's theory, in: Algebraic Number Fields by A. Fröhlich, Academic Press, London, 1977). In addition if we assume the Quillen–Lichtenbaum conjecture then
Soit l un nombre premier impair, soit F un corps de nombres totalement réel et soit E/F une extension abélienne de conducteur f, où E est un corps de nombres de type CM. Dans cette Note nous prouvons que pour tout entier impair n>0 et pour presque tout nombre premier l, où Sn(E/F,l) est l'idéal de Stickelberger (Ann. of Math. 135 (1992) 325–360 ; J. Coates, p-adic L-functions and Iwasawa's theory, in : Algebraic Number Fields by A. Fröhlich, Academic Press, London, 1977). Si nous supposons la conjecture de Quillen–Lichtenbaum alors
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Grzegorz Banaszak 1
@article{CRMATH_2003__337_9_575_0, author = {Grzegorz Banaszak}, title = {Higher analogues of {Stickelberger's} theorem}, journal = {Comptes Rendus. Math\'ematique}, pages = {575--580}, publisher = {Elsevier}, volume = {337}, number = {9}, year = {2003}, doi = {10.1016/j.crma.2003.09.019}, language = {en}, }
Grzegorz Banaszak. Higher analogues of Stickelberger's theorem. Comptes Rendus. Mathématique, Volume 337 (2003) no. 9, pp. 575-580. doi : 10.1016/j.crma.2003.09.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.09.019/
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