On the cyclotomic unit group and the ideal class group of a real abelian number field

DOI10.1006/jnth.1997.2086zbMath0879.11058OpenAlexW2770327461MaRDI QIDQ1358799

Manabu Ozaki

Publication date: 23 June 1997

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1997.2086

zbMATH Keywords

Galois modulesgroup of cyclotomic units\(p\)-Sylow subgroups of the ideal class groupcyclotomic \(\mathbb{Z}_ p\)-extensionreal abelian number field

Mathematics Subject Classification ID

Units and factorization (11R27) Class field theory (11R37) Iwasawa theory (11R23) Cyclotomic extensions (11R18)

Related Items (7)

On the cyclotomic unit group and the ideal class group of a real abelian number field. II ⋮ On the group of modular units and the ideal class group ⋮ Unnamed Item ⋮ Formules de classes pour les corps abéliens réels. (Class formulae for real Abelian fields) ⋮ Remark on elliptic units in a $\mathbb {Z}_p$-extension of an imaginary quadratic field ⋮ Cyclotomic units and class groups in _p-extensions of real abelian fields ⋮ Computation of the $p$-part of the ideal class group of certain real abelian fields

Cites Work

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• Class fields of abelian extensions of \(\mathbb Q\)
• Class groups of abelian fields, and the main conjecture
• The Iwasawa invariant \(\mu_p\) vanishes for abelian number fields
• On the Stickelberger ideal and the circular units of an abelian field
• Cohomology groups of cyclotomic units
• On relatively invariant circular units and Stickelberger elements
• On Γ-extensions of algebraic number fields
• On the Iwasawa Invariants of Totally Real Number Fields

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