Abelian 2-class field towers over the cyclotomic ℤ2-extensions of imaginary quadratic fields

Yasushi Mizusawa, Manabu Ozaki

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Abstract

For the cyclotomic ℤ2-extension k of an imaginary quadratic field k, we consider whether the Galois group G(k) of the maximal unramified pro-2-extension over k is abelian or not. The group G(k) is abelian if and only if the nth layer of the ℤ2-extension has abelian 2-class field tower for all n ≥ 1. The purpose of this paper is to classify all such imaginary quadratic fields k in part by using Iwasawa polynomials.

Original languageEnglish
Pages (from-to)437-453
Number of pages17
JournalMathematische Annalen
Volume347
Issue number2
DOIs
Publication statusPublished - 2010 Jan 1

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ASJC Scopus subject areas

  • Mathematics(all)

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