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# Functoriality of the Canonical Fractional Galois Ideal

Published:2010-07-06
Printed: Oct 2010
• Paul Buckingham,
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB
• Victor Snaith,
School of Mathematics and Statistics, The University of Sheffield, Western Bank, Sheffield, UK
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## Abstract

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.
 MSC Classifications: 11R42 - Zeta functions and $L$-functions of number fields [See also 11M41, 19F27] 11R23 - Iwasawa theory 11R70 - $K$-theory of global fields [See also 19Fxx]