\(p\)-rational fields, \(p\)-regular fields and restricted ramification

DOI10.5802/jtnb.98zbMath0957.11046OpenAlexW2331031825MaRDI QIDQ1320520

Jean-François Jaulent, Thong Nguyen Quang Do

Publication date: 1 April 2001

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1993__5_2_343_0

zbMATH Keywords

Leopoldt conjectureHilbert symbolsexplicit reciprocity lawnonabelian class field theorytamely unramified extensions

Mathematics Subject Classification ID

Galois theory (11R32) Class field theory (11R37) Iwasawa theory (11R23)

Related Items (18)

On the cohomological dimension of pro-\(p\)-extensions of number fields ⋮ On the \(T\)-ramified, \(S\)-split \(p\)-class field towers over an extension of degree prime to \(p\) ⋮ On the Galois structure of arithmetic cohomology. II: Ray class groups ⋮ Pro-\(\ell\)-extensions of \(\mathfrak l\)-rational number fields ⋮ On the cyclotomic norms and the Leopoldt and Gross-Kuz'min conjectures ⋮ \(p\)-adic approach of Greenberg's conjecture for totally real fields ⋮ A note on $p$-rational fields and the abc-conjecture ⋮ On the \(p\)-rationality of consecutive quadratic fields ⋮ Families of extensions of \(\mathfrak l\)-rational number fields ⋮ Cyclic extensions of degree \(\ell\) over an \(\ell\)-regular number field ⋮ Prime decomposition and the Iwasawa MU-invariant ⋮ 2-group of positive classes of a number field and wild kernel of \(K\)-theory. ⋮ Abelian prinicipalization of groups of logarithmic classes ⋮ Note on 2-rational fields ⋮ Triquadratic \(p\)-rational fields ⋮ Global \(\ell\)-adique clean field theory ⋮ The p-adic Kummer–Leopoldt constant: Normalized p-adic regulator ⋮ On the structure of the Galois group of the abelian closure of a number field

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Leopoldt's conjecture and Reiner's theorem
• On regular number fields
• On \(\mathbb{Z}_ p\)-torsion of some Galois modules
• Remarks on \(K_ 2\) of number fields
• On the Leopoldt conjecture on the p-adic regulators
• Lois de réciprocité primitives. (Primitive reciprocity laws)
• A subgroup theorem for free products of pro-finite groups
• Sur les p -extensions des corps p -rationnels
• Groupe de Galois de la p-extension abélienne p-ramifiée maximale d'un corps de nombres.
• Logarthme p-adique et groupes de Galois.

This page was built for publication: \(p\)-rational fields, \(p\)-regular fields and restricted ramification