An alternative approach to Kida and Ferrero's computations of Iwasawa λ-invariants

JOURNAL OF NUMBER THEORY

卷:138

Article

关键词: Iwasawa;    Lambda invariant;    Hurwitz formula;    Fermat prime;    Ferrero;    Kida;    Imaginary quadratic;   

DOI  :  10.1016/j.jnt.2013.11.014

来源: Elsevier

【 摘 要 】

We prove a slight generalization of Iwasawa's 'Riemann-Hurwitz' formula for number fields and use it to generalize Kida and Ferrero's well-known computations of Iwasawa lambda-invariants for the cyclotomic Z(2)-extensions of imaginary quadratic number fields. In particular, we show that if p is a Fermat prime, then similar explicit computations of Iwasawa lambda-invariants hold for certain imaginary quadratic extensions of the unique subfield k subset of Q(zeta(p2)) such that [k : Q] = P. In fact, we actually prove more by explicitly computing cohomology groups of principal ideals. The computation of lambda invariants obtained is a special case of a much more general result concerning relative lambda invariants for cyclotomic Z(2)-extensions of CM number fields due to Yuji Kida. However, the approach used here significantly differs from that of Kida, and the intermediate computations of cohomology groups found here do not hold in Kida's more general setting. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free