Number Theory
Higher analogues of Stickelberger's theorem
Comptes Rendus. Mathématique, Volume 337 (2003) no. 9, pp. 575-580.

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 S n (E/F,l) Ann l [G(E/F)] H 2 (𝒪 E [1/l]; l (n+1)) 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 S n (E/F,l) Ann l [G(E/F)] K 2n (𝒪 E ) l .

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 S n (E/F,l) Ann l [G(E/F)] H 2 (𝒪 E [1/l]; l (n+1)) 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 S n (E/F,l) Ann l [G(E/F)] K 2n (𝒪 E ) l .

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DOI: 10.1016/j.crma.2003.09.019
Banaszak, Grzegorz 1

1 Department of Mathematics, Adam Mickiewicz University, Poznań, Poland
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Banaszak, Grzegorz. 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. http://www.numdam.org/articles/10.1016/j.crma.2003.09.019/

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