Suppose that L/k is a finite and abelian extension such that k is a totally real base field and L is a CM-field. We regard the ideal class group Cl L, of L as a Gal(L/k)-module. As a sequel of the paper  by the first author, we study a problem whether the Stickelberger element for L/k times the annihilator ideal of the roots of unity in L is in the Fitting ideal of ClL, and also a problem whether it is in the Fitting ideal of the Pontrjagin dual (ClL)v. We systematically construct extensions L/k for which these properties do not hold, and also give numerical examples.
ASJC Scopus subject areas
- 数学 (全般)