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Kurihara established a refinement of the minus-part of the Iwasawa mainconjecture for totally real number fields using the higher Fitting ideals. Inthis paper, by using Kurihara's methods and Mazur-Rubin theory, we study thehigher Fitting ideals of the plus-part of Iwasawa modules associated thecyclotomic Z_p-extension of abelian fields for an odd prime number p. We definethe higher cyclotomic ideals C_i for any non-negative integer i, which areideals of the Iwasawa algebra defined by the Kolyvagin derivative classes ofcircular units, and prove that they give upper and lower bounds of the higherFitting ideals in some sense, and determine the pseudo-isomorphism classes ofthe plus-part of Iwasawa modules. Our result can be regarded as an partialanalogue of Kurihara's results and a refinement of the plus-part of the Iwasawamain conjecture for abelian fields.

On the higher Fitting ideals of Iwasawa modules of ideal class groups over real abelian fields