Some New Maps and Ideals in Classical Iwasawa Theory with Applications

Details Some New Maps and Ideals in Classical Iwasawa Theory with Applications Some New Maps and Ideals in Classical Iwasawa Theory with Applications

2009-05-27

arxiv.org/abs/0905.4336v3

Mathematics

Number Theory

36 pages. Several additions and improvements, principally: new title; new section on variation of K and kernel of {\mathfrak j

Scientific paper

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.

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