On higher Fitting ideals of Iwasawa modules of ideal class groups over imaginary quadratic fields and Euler systems of elliptic units

Abstract

Kurihara described all higher Fitting ideals of the minus part of Iwasawa modules of ideal class groups over totally real fields by using Stickelberger elements and Euler systems of “Gauss sums.” In this paper, we obtain some partial results for elliptic units which are analogues of his result. By using Kolyvagin derivative classes of Euler systems of elliptic units, we construct some ideals ${\mathfrak{C}}_{i,\chi }^{\mathrm{ell}}$ of Iwasawa algebras and prove that they give “upper bounds” of higher Fitting ideals of one- and two-variable Iwasawa modules of ideal class groups over imaginary quadratic fields.