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On metabelian 2-class field towers over $\mathbb Z_2$-extensions of real quadratic fields

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  06 October 2021

Yasushi Mizusawa Open the ORCID record for Yasushi Mizusawa [Opens in a new window]
Yasushi Mizusawa*
Affiliation:
Department of Mathematics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, 466-8555, Japan
*
e-mail: mizusawa.yasushi@nitech.ac.jp
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Abstract

We give a family of real quadratic fields such that the 2-class field towers over their cyclotomic $\mathbb Z_2$-extensions have metabelian Galois groups of abelian invariants $[2,2,2]$. We also consider the boundedness of the Galois groups in relation to Greenberg’s conjecture, and calculate their class-2 quotients with an explicit example.

Keywords

p-class field towerℤ p-extensionGreenberg’s conjecture

MSC classification

Primary: 11R23: Iwasawa theory
Secondary: 11R11: Quadratic extensions 11R32: Galois theory 11R37: Class field theory

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 3 , September 2022 , pp. 795 - 805
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Copyright
© Canadian Mathematical Society 2021

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