Some cases of the Fontaine-Mazur conjecture
type: Item
instance of: scholarly article
title: Some cases of the Fontaine-Mazur conjecture
zbMATH Open document ID: 0768.11044
DOI: 10.1016/0022-314X(92)90093-5
author: Nigel Boston
published in: Journal of Number Theory
publication date: 1993-01-17T00:00:00Z
review text: Let \(p\) be a prime, \(K\) an algebraic number field and \(L\) the maximal unramified \(p\)-extension of \(K\). Fontaine and Mazur have conjectured that there does not exist a \(p\)-adic representation of \(\text{Gal}(L/K)\) with infinite image. The author proves that the conjecture is true if \(K\) is a normal extension of prime degree \(l \neq p\) of a field \(F\) such that the class number of \(F\) is prime to \(p\).
Mathematics Subject Classification ID: 11R32
zbMATH DE Number: 98391
zbMATH Keywords: Fontaine-Mazur conjecture
zbMATH Keywords: absolute Galois group
zbMATH Keywords: nonexistence of an infinite everywhere unramified Galois pro-\(p\)-extension
zbMATH Keywords: \(p\)-saturated Galois group with integer values
zbMATH Keywords: \(p\)-adic representation
reviewed by: Helmut Koch
MaRDI profile type: Publication
Wikidata QID: Q123013800
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description: scientific article; zbMATH DE number 98391