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},\sqrt{-d...
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| creator | Habibi, Abdelaziz El Ziane, M'hammed |
| 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 $\mathbb{Q}(\sqrt{pq},\sqrt{-d})$. |
| doi_str_mv | 10.48550/arxiv.1804.10165 |
| format | Article |
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$\mathcal{X}=\mathcal{H}^{ab}=\mathrm{\mathrm{G}al}(K_{S\cup
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$\mathcal{X}=\mathcal{H}^{ab}=\mathrm{\mathrm{G}al}(K_{S\cup
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$\Lambda(G_{\infty,S})$-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
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| subjects | Mathematics - Number Theory |
| title | p-Rational Fields and the Structure of Some Modules |
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