Functoriality of the canonical fractional Galois ideal

Details Functoriality of the canonical fractional Galois ideal Functoriality of the canonical fractional Galois ideal

2008-03-19

arxiv.org/abs/0803.2781v1

Mathematics

K-Theory and Homology

28 pages

Scientific paper

The fractional Galois ideal of [Victor P. Snaith, Stark's conjecture and new Stickelberger phenomena, Canad. J. Math. 58 (2) (2006) 419--448] 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.

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