Iwasawa theory and Fitting ideals

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-infinity 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-infinity over F-infinity as a Z(p) [[Gal (Finfinity/Q)]]-module. We also study the Fitting ideals of the Selmer groups of an elliptic curve and certain Galois cohomology groups.