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A non-abelian Stickelberger theorem

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  01 July 2010

David Burns  and
Henri Johnston
David Burns
Affiliation:
Department of Mathematics, King’s College London, London WC2R 2LS, UK (email: [email protected])
Henri Johnston
Affiliation:
St John’s College, University of Cambridge, St John’s Street, Cambridge CB2 1TP, UK (email: [email protected])
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Abstract

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Let L/k be a finite Galois extension of number fields with Galois group G. For every odd prime p satisfying certain mild technical hypotheses, we use values of Artin L-functions to construct an element in the centre of the group ring ℤ(p)[G] that annihilates the p-part of the class group of L.

Keywords

equivariant L-valuesclass groups

MSC classification

Secondary: 11R29: Class numbers, class groups, discriminants 11R42: Zeta functions and $L$-functions of number fields 11R33: Integral representations related to algebraic numbers; Galois module structure of rings of integers
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 1 , January 2011 , pp. 35 - 55
Copyright
Copyright © Foundation Compositio Mathematica 2010

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