Higher analogues of Stickelberger's theorem

Authors:

• Grzegorz Marian Banaszak

Abstract

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 _{ℤl[G(E/F ]} H ² (O _E [1/l]; ℤ _l (n + 1)) where S _n (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 _ℤl[G(E/F)] K _2n (O _E ) _l . © 2003 Académie des sciences. Published by Éditions scientifiques et médicales Elsevier SAS. All rights reserved.