The structure of the unramified abelian Iwasawa module of some number fields

Ali Mouhib

Vol. 323 (2023), No. 1, 173–184

DOI: 10.2140/pjm.2023.323.173

Abstract

For a given positive integer $m$, we determine an explicit infinite family of real quadratic number fields $F$, such that the unramified abelian Iwasawa module over the ${\mathbb{Z}}_2$-extension of $F$, is isomorphic to ${(\mathbb{Z}∕2\mathbb{Z})}^{2^m}$.

Keywords

class group, unit group, capitulation problem, $Z_2$-extension

Mathematical Subject Classification

Primary: 11R23, 11R29, 11R32, 11R37

Milestones

Received: 25 October 2022

Revised: 28 February 2023

Accepted: 1 April 2023

Published: 29 May 2023