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June 2012 The commutativity of Galois groups of the maximal unramified pro-$p$-extensions over the cyclotomic $\mathbb{Z}_{p}$-extensions II
Keiji Okano
Osaka J. Math. 49(2): 271-295 (June 2012).

Abstract

Let $p$ be an odd prime number and $K_{\infty}$ the cyclotomic $\mathbb{Z}_{p}$-extension of a Galois $p$-extension $K$ over an imaginary quadratic field. We consider the Galois group $\tilde{X}(K_{\infty})$ of the maximal unramified pro-$p$-extension of $K_{\infty}$. In this paper, under certain assumptions, we give certain $K$ such that $\tilde{X}(K_{\infty})$ is abelian. Also, we give an example such that a special value of the characteristic polynomial of the Iwasawa module of $K_{\infty}$ determines whether $\tilde{X}(K_{\infty})$ is abelian or not.

Citation

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Keiji Okano. "The commutativity of Galois groups of the maximal unramified pro-$p$-extensions over the cyclotomic $\mathbb{Z}_{p}$-extensions II." Osaka J. Math. 49 (2) 271 - 295, June 2012.

Information

Published: June 2012
First available in Project Euclid: 20 June 2012

zbMATH: 1333.11101
MathSciNet: MR2887619

Subjects:
Primary: 11R23
Secondary: 11R37

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics

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Vol.49 • No. 2 • June 2012
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