On the Galois module structure over CM-fields

DOI10.1007/BF02567089zbMath0757.11044MaRDI QIDQ1197372

Jan Brinkhuis

Publication date: 16 January 1993

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155728

zbMATH Keywords

Galois module structureCM-fieldtame realizationunramified realizations

Mathematics Subject Classification ID

Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33)

Related Items (8)

On a relative normal integral basis problem over abelian number fields ⋮ Unramified quadratic extensions of real quadratic fields, normal integral bases, and 2-adic \(L\)-functions ⋮ Normal integral bases and strict ray class groups modulo 4 ⋮ Relative Galois module structure of rings of integers of absolutely abelian number fields ⋮ Galois module structure as the obstruction to a local-global principle ⋮ The Galois module structure of certain arithmetic principal homogeneous spaces ⋮ On quadratic subextensions of ray class fields of quadratic fields mod \({\mathfrak p}\) ⋮ Normal integral bases of \(\infty\)-ramified abelian extensions of totally real number fields.

Cites Work

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• Bases normales, unités et conjecture faible de Leopoldt. (Normal bases, units, and the weak Leopoldt conjecture)
• \(\mathbb Z_p\)-extensions of complex multiplication fields
• On Vandiver's conjecture and \({\mathbb{Z}}_ p\)-extensions of \({\mathbb{Q}}(\zeta_{p^ n})\)
• On Fröhlich's conjecture for rings of integers of tame extensions
• Galois module structure as the obstruction to a local-global principle
• Normal integral bases and complex conjugation.
• Galois module structure of abelian extensions.
• Unramified Abelian Extensions of CM -Fields and their Galois Module Structure
• The Group of Unramified Kummer Extensions of Prime Degree

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