On the Leopoldt conjecture on the p-adic regulators

DOI10.1016/0022-314X(87)90073-4zbMath0621.12009WikidataQ123009471 ScholiaQ123009471MaRDI QIDQ1090366

Hiroo Miki

Publication date: 1987

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

Galois groupLeopoldt's conjecturep-adic regulatormaximal p-ramified abelian p-extension

Mathematics Subject Classification ID

Units and factorization (11R27) Cyclotomic extensions (11R18) Galois cohomology (11R34)

Related Items

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, Sur les p -extensions des corps p -rationnels, Cohomology of normic systems and fake \(\mathbb{Z}_p\)-extensions, Cyclic extensions of prime degree and their \(p\)-adic regulators, On regular number fields, Note on 2-rational fields, Valuations of \(p\)-adic regulators of cyclic cubic fields, Global \(\ell\)-adique clean field theory, A sufficient condition for Leopoldt's conjecture, Greenberg's conjecture and Leopoldt's conjecture, Some remarks on Leopoldt's conjecture, \(p\)-rational fields, \(p\)-regular fields and restricted ramification

Cites Work

• A note on the group of units of an algebraic number field
• On \(\mathbb Z_{\ell}\)-extensions of algebraic number fields
• Galois Group of the Maximal Abelian Extension over an Algebraic Number Field
• Groupe de Galois de la p-extension abélienne p-ramifiée maximale d'un corps de nombres.
• On the Iwasawa Invariants of Totally Real Number Fields
• On the maximal abelianℓ-extension of a finite algebraic number field with given ramification
• Linear forms in the logarithms of algebraic numbers
• On the units of algebraic number fields
• Extensions with given points of ramification
• Zur Arithmetik in abelschen Zahlkörpern.
• On the units of an algebraic number field