p-Rational Fields and the Structure of Some Modules

p-Rational Fields and the Structure of Some Modules

Assume that the field \(K\) is \(p\)-rational. We study the freeness of the \(\Lambda(G_{\infty,S})\)-module \(\mathcal{X}=\mathcal{H}^{ab}=\mathrm{\mathrm{G}al}(K_{S\cup S_p}/K_{\infty,S})^{ab}\). For numerical evidence to our result we consider the case of fields of the form \(\mathbb{Q}(\sqrt{pq}...

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Veröffentlicht in:arXiv.org 2018-04
Hauptverfasser: Abdelaziz El Habibi, Ziane, M'hammed
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description Assume that the field \(K\) is \(p\)-rational. We study the freeness of the \(\Lambda(G_{\infty,S})\)-module \(\mathcal{X}=\mathcal{H}^{ab}=\mathrm{\mathrm{G}al}(K_{S\cup S_p}/K_{\infty,S})^{ab}\). For numerical evidence to our result we consider the case of fields of the form \(\mathbb{Q}(\sqrt{pq},\sqrt{-d})\).
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title p-Rational Fields and the Structure of Some Modules
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