S ep 2 00 9 Some New Ideals in Classical Iwasawa Theory
نویسنده
چکیده
We introduce a new ideal D of the p-adic Galois group-ring associated to a real abelian field and a related ideal 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 J is linked by explicit reciprocity to a third ideal S studied more generally in [So3]. 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.
منابع مشابه
Some New Ideals in Classical Iwasawa Theory
We construct an analogue of the Stickelberger ideal for real abelian fields by means of cyclotomic units and a Kummer-type pairing with values in a completed p-adic group-ring. We give several different descriptions of this ideal, prove the analogue of Stickelberger's Theorem using Thaine's methods and establish links with certain Fitting ideals in a particular case. Our construction fits into ...
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