On circular units over the cyclotomic Zp-Extension of an abelian field

Research output: Contribution to journalArticle

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Abstract

Let K be an abelian number field of conductor f and p a prime. Sinnott defined circular units CK s of K using the norm maps from the cyclotomic units of the nth cyclotomic fields for all n and Washington defined circular units CK w of K to be the Galois invariant of the cyclotomic units of the f th cyclotomic field. In this note, we investigate a question raised by Kolster in [5] of whether the projective limits of circular units of Sinnott and Washington over the cyclotomic Z p-extension of K are equal. Belliard [2] and Kučera [6] found independently some counter examples to this question. The purpose of this note is to find some conditions on the ground field K under which Kolster's question has an affirmative answer.

Original languageEnglish
Pages (from-to)117-123
Number of pages7
JournalManuscripta Mathematica
Volume115
Issue number1
DOIs
Publication statusPublished - 2004 Sep 1

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Cyclotomic
Unit
Cyclotomic Fields
Projective Limit
Galois
Conductor
Number field
Counterexample
Norm
Invariant

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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On circular units over the cyclotomic Zp-Extension of an abelian field. / Seo, Soogil.

In: Manuscripta Mathematica, Vol. 115, No. 1, 01.09.2004, p. 117-123.

Research output: Contribution to journalArticle

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