### Abstract

Let K be an abelian number field of conductor f and p a prime. Sinnott defined circular units C_{K}^{s} of K using the norm maps from the cyclotomic units of the nth cyclotomic fields for all n and Washington defined circular units C_{K}^{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 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)

### Cite this

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_{p}-Extension of an abelian field',

*Manuscripta Mathematica*, vol. 115, no. 1, pp. 117-123. https://doi.org/10.1007/s00229-004-0490-9

**On circular units over the cyclotomic Z _{p}-Extension of an abelian field.** / Seo, Soogil.

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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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 -