On the Galois structure of circular units in \(\mathbb{Z}_p\)-extensions

DOI10.1006/jnth.1997.2200zbMath0911.11051OpenAlexW2004761329MaRDI QIDQ1267290

Jean-Robert Belliard

Publication date: 5 May 1999

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

Full work available at URL: https://doi.org/10.1006/jnth.1997.2200

zbMATH Keywords

cohomologyGalois module structurecircular unitsuniversal normsreal abelian fieldcyclotomic \(\mathbb{Z}_p\)-extensioncyclotomic towerGalois behaviour

Mathematics Subject Classification ID

Iwasawa theory (11R23) Cyclotomic extensions (11R18) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33) Galois cohomology (11R34)

Related Items (6)

Cyclotomic units and Stickelberger ideals of global function fields ⋮ SUR LA CONJECTURE FAIBLE DE GREENBERG DANS LE CAS ABÉLIEN p-DÉCOMPOSÉ ⋮ Truncated Euler Systems over Imaginary Quadratic Fields ⋮ Stark units in \(\mathbb{Z}_p\)-extensions ⋮ Formules de classes pour les corps abéliens réels. (Class formulae for real Abelian fields) ⋮ ASYMPTOTIC COHOMOLOGY OF CIRCULAR UNITS

Uses Software

• PARI/GP

Cites Work

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• 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
• Galois relations for cyclotomic numbers and \(p\)-units
• Cyclotomic units in \(\mathbb Z_p\)-extensions
• On a construction of \(p\)-units in abelian fields
• On universal norms in \(\mathbb{Z}_ p\)-extensions
• On the Stickelberger ideal and circular units of a compositum of quadratic fields
• On relations between cyclotomic units
• Units in real Abelian fields.
• Generators and Relations for Cyclotomic Units
• On the units of algebraic number fields

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