On the Hilbert $2$-class field towers of some cyclotomic ${\mathbb{Z}}_2$-extensions

Abstract

In this paper, we study the length of the $2$-class field towers and the structure of the Galois groups $\mathrm{Gal}(\mathcal{L}(K_n)/K_n)$ of the maximal unramified $2$-extensions of the layers $K_n$ of the cyclotomic ${\mathbb{Z}}_2$-extension of some special Dirichlet fields. The capitulation problem is investigated too.

15 pages

References in corpus (2)

• The rank of the 2-class group of some fields with large degree
• $2$-class groups of cyclotomic towers of imaginary biquadratic fields and applications

Cited by in corpus (1)

• Greenberg's conjecture and Iwasawa module of Real biquadratic fields I