We introduce a new ideal of the p-adic Galois group-ring associated to a real abelian field and a related ideal for imaginary abelian fields, Both result from an equivariant, Kummer-type pairing applied to Stark units in a -tower of abelian fields, and is linked by explicit reciprocity to a third ideal studied more generally in [D. Solomon, Acta Arith. 143 (2010)]. 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 Λ-torsion submodules, and a new exact sequence related to the Main Conjecture.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-2-1,
author = {David Solomon},
title = {Some new maps and ideals in classical Iwasawa theory with applications},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {101-140},
zbl = {1292.11122},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-2-1}
}
David Solomon. Some new maps and ideals in classical Iwasawa theory with applications. Acta Arithmetica, Tome 166 (2014) pp. 101-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-2-1/