On the 2-part of the ideal class group of the cyclotomic \(\mathbb Z_p\)-extension over the rationals

DOI10.1007/S12188-010-0036-XzbMath1222.11126OpenAlexW2025215331MaRDI QIDQ609394

Shoichi Nakajima, Humio Ichimura

Publication date: 30 November 2010

Published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12188-010-0036-x

zbMATH Keywords

class groupsclass numberscyclotomic fields

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Iwasawa theory (11R23) Cyclotomic extensions (11R18)

Related Items (7)

Biographical Sketch of Professor Humio Ichimura ⋮ The \(l\)-class group of the \(\mathbb Z_p\)-extension over the rational field ⋮ A note on the relative class number of the cyclotomic \(\mathbb Z_p\)-extension of \(\mathbb Q(\sqrt{-p})\). ⋮ Class numbers in cyclotomic \(\mathbb{Z}_p\)-extensions ⋮ An alternative approach to Kida and Ferrero's computations of Iwasawa \(\lambda\)-invariants ⋮ Tate-Shafarevich groups in the cyclotomic \(\hat{\mathbb{Z}} \)-extension and Weber's class number problem ⋮ On the 2-part of the class numbers of cyclotomic fields of prime power conductors

Cites Work

• Unnamed Item
• Unnamed Item
• The ideal class group of the basic \(\mathbb Z_p\)-extension over an imaginary quadratic field
• Primary components of the ideal class group of the \(\mathbb Z_p\)-extension over \(\mathbb Q\) for typical inert primes
• Class numbers and \(\mathbb Z_p\)-extensions
• The non-p-part of the class number in a cyclotomic \(\mathbb{Z}_p\)-extension
• Certain primary components of the ideal class group of the \(\mathbb Z_p\)-extension over the rationals
• Ideal Class Groups of Iwasawa-Theoretical Abelian Extensions Over the Rational Field
• The narrow class groups of some Z_p-extensions over the rationals
• On the parity of the class number of the 7nth cyclotomic field
• Classnumbers and unit signatures
• Abschätzungen für die Klassenzahlen der quadratischen Körper

This page was built for publication: On the 2-part of the ideal class group of the cyclotomic \(\mathbb Z_p\)-extension over the rationals