### 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 ℤ_{P}-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 language | English |
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Pages (from-to) | 39-86 |

Number of pages | 48 |

Journal | Journal fur die Reine und Angewandte Mathematik |

Issue number | 561 |

Publication status | Published - 2003 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Kurihara, M. (2003). Iwasawa theory and fitting ideals.

*Journal fur die Reine und Angewandte Mathematik*, (561), 39-86.