Some New Maps and Ideals in Classical Iwasawa Theory with Applications
Abstract
We introduce a new ideal {\mathfrak D} of the p-adic Galois group-ring associated to a real abelian field and a related ideal {\mathfrak J} for imaginary abelian fields. Both result from an equivariant, Kummer-type pairing applied to Stark units in a Z_p-tower of abelian fields and {\mathfrak J} is linked by explicit reciprocity to a third ideal {\mathfrak S} studied more generally in a previous work. This leads to a new and unifying framework for the Iwasawa Theory of such fields including a real analogue of Stickelberger's Theorem, links with certain Fitting ideals and \Lambda-torsion submodules, and a new exact sequence related to the Main Conjecture.
Keywords
Cite
@article{arxiv.0905.4336,
title = {Some New Maps and Ideals in Classical Iwasawa Theory with Applications},
author = {David Solomon},
journal= {arXiv preprint arXiv:0905.4336},
year = {2010}
}
Comments
36 pages. Several additions and improvements, principally: new title; new section on variation of K and kernel of {\mathfrak j}; more detail on links with Greenberg's Conjecture; more on {\Lambda}-torsion including more explicit determination of {\Lambda}-torsion submodule of {\mathfrak X}_\infty; various remarks added