Ideal class groups in basic \(\mathbb Z_{p_1}\times\dots\times\mathbb Z_{p_s}\)-extensions of abelian number fields

DOI10.1007/BF01396627zbMath0495.12007MaRDI QIDQ1169509

Eduardo C. Friedman

Publication date: 1982

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142858

zbMATH Keywords

ideal class groupsabelian number fieldsGreenberg conjecturebasic Zp-extensionsvanishing of Iwasawa mu invariant

Mathematics Subject Classification ID

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

Related Items (12)

Triviality of Iwasawa module associated to some abelian fields of prime conductors ⋮ \(\Gamma\)-transforms of rational function measures on \(\mathbb Z_ S\) ⋮ Growth of class numbers in \({\mathbb{Z}}_{\ell}\)-extensions connected with imaginary quadratic fields ⋮ On the Iwasawa lambda invariant of an imaginary abelian field of conductor \(3p^{n+1}\) ⋮ Signature ranks of units in cyclotomic extensions of abelian number fields ⋮ Unnamed Item ⋮ On the class numbers of cyclotomic fields ⋮ ON THE 2-ADIC IWASAWA LAMBDA INVARIANTS OF THE p-CYCLOTOMIC FIELDS AND THEIR QUADRATIC TWISTS ⋮ On the \(\mu\)-invariant of the \(\Gamma\)-transform of a rational function ⋮ Congruences for special values of L-functions of elliptic curves with complex multiplication ⋮ An analogue of the Washington-Sinnott theorem for elliptic curves with complex multiplication I ⋮ Modular symbols, Eisenstein series, and congruences

Cites Work

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• The Iwasawa invariant \(\mu_p\) vanishes for abelian number fields
• Class numbers and \(\mathbb Z_p\)-extensions
• The non-p-part of the class number in a cyclotomic \(\mathbb{Z}_p\)-extension
• On \(\mathbb Z_{\ell}\)-extensions of algebraic number fields
• On Γ-extensions of algebraic number fields
• On the Iwasawa Invariants of Totally Real Number Fields

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