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
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.
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