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

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Let K be an abelian number field of conductor f and p a prime. Sinnott defined circular units CKs of K using the norm maps from the cyclotomic units of the nth cyclotomic fields for all n and Washington defined circular units CKw 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
Issue number1
Publication statusPublished - 2004 Sept

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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