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arXiv · 0905.4336

Some New Maps and Ideals in Classical Iwasawa Theory with Applications

David Solomon
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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 Λ-torsion submodules, and a new exact sequence related to the Main Conjecture.

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David Solomon. 2010-08-03. Some New Maps and Ideals in Classical Iwasawa Theory with Applications. https://arxiv.org/abs/0905.4336

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