TY - JOUR
T1 - Ideal class groups of CM-fields with non-cyclic galois action
AU - Kurihara, Masato
AU - Miura, Takashi
PY - 2012/12
Y1 - 2012/12
N2 - 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 [8] 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.
AB - 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 [8] 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.
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U2 - 10.3836/tjm/1358951328
DO - 10.3836/tjm/1358951328
M3 - Article
AN - SCOPUS:84890189154
SN - 0387-3870
VL - 35
SP - 411
EP - 439
JO - Tokyo Journal of Mathematics
JF - Tokyo Journal of Mathematics
IS - 2
ER -