p-Rational Fields and the Structure of Some Modules
26 Apr 2018
•
Habibi Abdelaziz El
•
Ziane M'hammed
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 $\mathbb{Q}(\sqrt{pq},\sqrt{-d})$.(read more)