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

Yasushi Mizusawa, Manabu Ozaki

Research output: Contribution to journalArticle

3 Citations (Scopus)

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
Externally publishedYes

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Imaginary Quadratic Field
Cyclotomic
Galois group
Classify
If and only if
Polynomial
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Abelian 2-class field towers over the cyclotomic ℤ2-extensions of imaginary quadratic fields. / Mizusawa, Yasushi; Ozaki, Manabu.

In: Mathematische Annalen, Vol. 347, No. 2, 2010, p. 437-453.

Research output: Contribution to journalArticle

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