A remark on Boston's question concerning the existence of unramified \(p\)-extensions. II
In a previous paper [\textit{A. Nomura}, J. Number Theory 58, 66-70 (1996; Zbl 0856.11052)]\ the author constructed \(p\)-extensions of number fields \(K\) with degree \((K:\mathbb Q)\) coprime to \(p\) which gave a positive answer to a question of N. Boston. Here, the author constructs a similar family of extensions in the case where \((K:\mathbb Q)\) is divisible by \(p\). As a corollary, he proves that the Fontaine-Mazur conjecture holds for certain \(p\)-extensions of \(\mathbb Q\).
scientific article; zbMATH DE number 1022283