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

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

2011-03-17

arxiv.org/abs/1103.3384v2

Mathematics

Number Theory

43 pages

Scientific paper

In this paper, we study the higher Fitting ideals of the even character part of the Iwasawa modules of ideal class groups. We treat an arbitrary prime number p (p is not necessarily odd), an arbitrary abelian extention field K/Q which is totally real and unramified at p, and an arbitrary non-trivial even character of Gal(K(\mu_p/Q)). We construct two types of ideals C_{i,\chi} and \Theta^{cu}_{i,\chi} of the Iwasawa algebra \Lambda_\chi by using Sinnott's circular units units. We prove that the ideal C_{i,\chi} gives an upper bound of the i-th Fitting ideal, and some patial results on the relation between C_{i,\chi}, \Theta^{cu}_{i,\chi} and lower bounds of the higher Fitting ideals. Our results are analogues of Kurihara's result, which treats the odd character part, and can be regarded as a refinement of the Iwasawa main conjecture for the even character part.

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