\(\ell\)-class groups of fields in Kummer towers

DOI10.5565/PUBLMAT6612210zbMath1490.11108arXiv1905.04966MaRDI QIDQ2075308

Yue Xu, Yi Ouyang, Shenxing Zhang, Jianing Li

Publication date: 14 February 2022

Published in: Publicacions Matemàtiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.04966

zbMATH Keywords

class groupsgenus theoryChevalley's ambiguous class number formula

Mathematics Subject Classification ID

Quadratic extensions (11R11) Class numbers, class groups, discriminants (11R29)

Related Items (3)

On the λ-stability of p-class groups along cyclic p-towers of a number field ⋮ The Chevalley-Herbrand formula and the real abelian Main Conjecture (new criterion using capitulation of the class group) ⋮ On \(p\)-class groups of relative cyclic \(p\)-extensions

Cites Work

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• A note on class numbers of algebraic number fields
• On cyclotomic \(\mathbb{Z}_2\)-extensions of imaginary quadratic fields
• Remarks on \(\mathbb{Z}_ p\)-extensions of number fields
• On the ramification of Hecke algebras at Eisenstein primes
• The 3-class groups of \(\mathbb{Q}(\sqrt[3{p})\) and its normal closure]
• The Chevalley-Gras formula over global fields
• On class numbers of pure quartic fields
• Invariant generalized ideal classes -- structure theorems for \(p\)-class groups in \(p\)-extensions
• Pure cubic fields whose class numbers are multiples of three
• Fundamental units of real quadratic fields of odd class number
• A genus theory for quartic fields.
• Ranks of 3-class groups of non-Galois cubic fields
• Estimating class numbers over metabelian extensions
• On 3-Class groups of certain pure cubic fields

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