A remark on Boston's question concerning the existence of unramified \(p\)-extensions. II (Q1357057)
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scientific article; zbMATH DE number 1022283
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark on Boston's question concerning the existence of unramified \(p\)-extensions. II |
scientific article; zbMATH DE number 1022283 |
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A remark on Boston's question concerning the existence of unramified \(p\)-extensions. II (English)
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16 November 1997
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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 \(\mathbb Q\).
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Fontaine-Mazur conjecture
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class field tower
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pro-\(p\)-extensions
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