Some Cases of the Fontaine–Mazur Conjecture, II

Boston, Nigel

doi:10.1006/jnth.1998.2337

Cited by 22 publications

(14 citation statements)

References 16 publications

(29 reference statements)

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“…It has been proven in special situations, cf. [1,7,14] (for the case S = ∅) and [13]. In this section, using Corollary 5, we give the following equivalent formulation:…”

Section: On the Fontaine-mazur Conjecturementioning

confidence: 99%

On $p$-class groups and the Fontaine-Mazur conjecture

Gärtner

2014

Mathematical Research Letters

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Abstract. Answering a question by Stark, we show that for an infinite unramified pro-p-extension of a number field k, the p-class numbers of its finite subextensions tend to infinity. This is proven by means of a group-theoretical result on compact p-adic analytic groups. Furthermore, we provide an equivalent formulation of the FontaineMazur conjecture for p-extensions unramified outside a finite set of primes not containing any prime above p.

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“…It has been proven in special situations, cf. [1,7,14] (for the case S = ∅) and [13]. In this section, using Corollary 5, we give the following equivalent formulation:…”

Section: On the Fontaine-mazur Conjecturementioning

confidence: 99%

On $p$-class groups and the Fontaine-Mazur conjecture

Gärtner

2014

Mathematical Research Letters

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“…On peut alors vérifier que G ab S Z 4 2 × Z/2Z. En particulier, K vérifie la S-condition arithmétique.…”

Section: Le Premierétage De K ∞ /Kunclassified

“…Par exemple, si S est un ensemble fini de places de K ne contenant aucune place au-dessus de p, la conjecture de Fontaine-Mazur (cf. [5], [3], [4], ...) indique que toute représentation continue ρ : G S → Gl m (Z p ) a une image finie, où G S = Gal(K S /K), K Sé tant donc la pro-p-extension maximale de K non-ramifiée en dehors de S. Alors qu'au contraire, si S contient toutes les places au-dessus de p, l'extension cyclotomique montre que G S a au moins un quotient p-analytique infini. Autre différence.…”

Section: Introductionunclassified

Sur la dimension cohomologique des pro-p-extensions des corps de nombres

Maire¹

2005

J. Théor. Nombres Bordeaux

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“…There are a couple of equivalent forms of this conjecture [8]. Let G K,S (p) denote the Galois group over K of the maximal p-extension unramified outside S. A (finitely generated) pro-p group is called analytic if it embeds in GL n (Q p ) for some n.…”

Section: Introductionmentioning

confidence: 99%