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.
|Number of pages||48|
|Journal||Journal fur die Reine und Angewandte Mathematik|
|Publication status||Published - 2003|
ASJC Scopus subject areas