Abstract
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 language | English |
|---|---|
| Pages (from-to) | 117-123 |
| Number of pages | 7 |
| Journal | Manuscripta Mathematica |
| Volume | 115 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2004 Sep 1 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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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 journal › Article
TY - JOUR
T1 - On circular units over the cyclotomic Zp-Extension of an abelian field
AU - Seo, Soogil
PY - 2004/9/1
Y1 - 2004/9/1
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=4744356207&partnerID=8YFLogxK
U2 - 10.1007/s00229-004-0490-9
DO - 10.1007/s00229-004-0490-9
M3 - Article
AN - SCOPUS:4744356207
VL - 115
SP - 117
EP - 123
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
SN - 0025-2611
IS - 1
ER -