The class group of \(\mathbb{Z}_p\)-extensions over totally real number fields

DOI10.2748/tmj/1178225114zbMath0896.11044OpenAlexW2091841918MaRDI QIDQ1384454

Manabu Ozaki

Publication date: 24 September 1998

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178225114

zbMATH Keywords

capitulationGreenberg's conjecture\(p\)-class groupspro-\(p\)-extensions\(p\)-adic zeta function\(\mathbb{Z}_p\)-extensions over totally real number fields\(p\)-class number

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Iwasawa theory (11R23)

Related Items (9)

Genus formulas and Greenberg's conjecture ⋮ On Greenberg's generalized conjecture for CM-fields ⋮ Some remarks on finite submodules of the unramified Iwasawa module of totally real fields ⋮ Some remarks on pseudo-null submodules of tamely ramified Iwasawa modules ⋮ Tamely ramified Iwasawa modules having no non-trivial pseudo-null submodules ⋮ On \(p\)-adic \(L\)-functions and \(\mathbb{Z}_p\)-extensions of certain real abelian number fields ⋮ Ideal norms in the cyclotomic tower and Greenberg's conjecture ⋮ On pseudo-null Iwasawa modules ⋮ On families of imaginary abelian fields with pseudo-null unramified Iwasawa modules

Cites Work

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• On the structure of certain Galois groups
• Remarks on \(\mathbb{Z}_ p\)-extensions of number fields
• On \(\mathbb Z_{\ell}\)-extensions of algebraic number fields
• A note on the capitulation in \(\mathbb{Z}_ p\)-extensions
• The Iwasawa conjecture for totally real fields
• Class numbers of certain real abelian fields

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