Iwasawa theory and fitting ideals

Research output: Contribution to journalArticle

27 Citations (Scopus)

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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Iwasawa Theory
Galois group
CM-field
Galois Cohomology
Selmer Group
Ideal Class Group
Cyclotomic
Cohomology Group
Elliptic Curves
Module

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Iwasawa theory and fitting ideals. / Kurihara, Masato.

In: Journal fur die Reine und Angewandte Mathematik, No. 561, 2003, p. 39-86.

Research output: Contribution to journalArticle

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