Triviality in ideal class groups of Iwasawa-theoretical abelian number fields

DOI10.2969/jmsj/1158241937zbMath1160.11357OpenAlexW2025107438MaRDI QIDQ2569283

Kuniaki Horie

Publication date: 18 October 2005

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2969/jmsj/1158241937

zbMATH Keywords

ideal class groupabelian number fields

Mathematics Subject Classification ID

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

Related Items (7)

WEBER'S CLASS NUMBER PROBLEM IN THE CYCLOTOMIC ℤ₂-EXTENSION OF ℚ, III ⋮ Triviality of Iwasawa module associated to some abelian fields of prime conductors ⋮ On the Iwasawa lambda invariant of an imaginary abelian field of conductor \(3p^{n+1}\) ⋮ Weber's class number problem in the cyclotomic \(\mathbb Z_2\)-extension of \(\mathbb Q\). II. ⋮ On the class number of a real abelian field of prime conductor ⋮ 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

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