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Functoriality of the Canonical Fractional Galois Ideal

Published online by Cambridge University Press:  20 November 2018

Paul Buckingham  and
Victor Snaith
Paul Buckingham*
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB
Victor Snaith*
Affiliation:
School of Mathematics and Statistics, The University of Sheffield, Western Bank, Sheffield, UK
*
p.r.buckingham@ualberta.ca
V.Snaith@sheffield.ac.uk
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Abstract

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The fractional Galois ideal is a conjectural improvement on the higher Stickelberger ideals defined at negative integers, and is expected to provide non-trivial annihilators for higher $K$-groups of rings of integers of number fields. In this article, we extend the definition of the fractional Galois ideal to arbitrary (possibly infinite and non-abelian) Galois extensions of number fields under the assumption of Stark's conjectures and prove naturality properties under canonical changes of extension. We discuss applications of this to the construction of ideals in non-commutative Iwasawa algebras.

Keywords

11R4211R2311R70
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 5 , 01 October 2010 , pp. 1011 - 1036
Copyright
Copyright © Canadian Mathematical Society 2010

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