Functoriality of the canonical fractional Galois ideal

Abstract

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.

29 pages. Updated to include a comment in the introduction about a problem with Proposition 3.6 that the authors have not been able to resolve

References in corpus (3)

• The GL_2 main conjecture for elliptic curves without complex multiplication
• The canonical fractional Galois ideal at s=0
• On the Iwasawa theory of p-adic Lie extensions

Cited by in corpus (2)

• The canonical fractional Galois ideal at s=0
• The fractional Galois ideal for arbitrary order of vanishing