Iwasawa theory and fitting ideals

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Abstract

By studying the Fitting ideals of the minus parts of the ideal class groups of CM fields, we give a more precise relationship than the usual main conjecture between the analytic side and the algebraic side. In particular, for the cyclotomic ℤP-extension F of an abelian field F, we determine the initial Fitting ideal of the minus part of the Galois group of the maximal unramified abelian pro-p-extension of F, over F as a Z p[[Ga[(F∞/ℚ)]]-module. We also study the Fitting ideals of the Selmer groups of an elliptic curve and certain Galois cohomology groups.

Original languageEnglish
Pages (from-to)39-86
Number of pages48
JournalJournal fur die Reine und Angewandte Mathematik
Issue number561
Publication statusPublished - 2003
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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