A note on circular units in ℤ p -extensions

Radan Kučera

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 1, page 223-229
  • ISSN: 1246-7405

Abstract

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In this note we consider projective limits of Sinnott and Washington groups of circular units in the cyclotomic ℤ p -extension of an abelian field. A concrete example is given to show that these two limits do not coincide in general.

How to cite

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Kučera, Radan. "A note on circular units in $\mathbb {Z}_p$-extensions." Journal de théorie des nombres de Bordeaux 15.1 (2003): 223-229. <http://eudml.org/doc/249069>.

@article{Kučera2003,
abstract = {In this note we consider projective limits of Sinnott and Washington groups of circular units in the cyclotomic $\mathbb \{Z\}_p$-extension of an abelian field. A concrete example is given to show that these two limits do not coincide in general.},
author = {Kučera, Radan},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {cyclotomic units},
language = {eng},
number = {1},
pages = {223-229},
publisher = {Université Bordeaux I},
title = {A note on circular units in $\mathbb \{Z\}_p$-extensions},
url = {http://eudml.org/doc/249069},
volume = {15},
year = {2003},
}

TY - JOUR
AU - Kučera, Radan
TI - A note on circular units in $\mathbb {Z}_p$-extensions
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 1
SP - 223
EP - 229
AB - In this note we consider projective limits of Sinnott and Washington groups of circular units in the cyclotomic $\mathbb {Z}_p$-extension of an abelian field. A concrete example is given to show that these two limits do not coincide in general.
LA - eng
KW - cyclotomic units
UR - http://eudml.org/doc/249069
ER -

References

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  1. [B] J.-R. Belliard, Sous-modules d'unités en théorie d'Iwasawa, to appear in Publications mathématiques de l'Université de Franche-Comté. MR1987282
  2. [GK] R. Gold, J. Kim, Bases for cyclotomic units. Compositio Math.71 (1989), 13-27. Zbl0687.12003MR1008802
  3. [KN] R. Kučera, J. Nekovář, Cyclotomic units in Zp-extensions. J. Algebra171 (1995), 457-472. Zbl0824.11071MR1315907
  4. [L] G. Lettl, A note on Thaine's circular units. J. Number Theory35 (1970), 224-226. Zbl0705.11064MR1057325
  5. [R] K. Rubin, The main conjecture, appendix in S. Lang, Cyclotomic Fields I and II, Springer-Verlag, New York, 1990. Zbl0704.11038MR1029028
  6. [S] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field. Invent. Math.62 (1980), 181-234. Zbl0465.12001MR595586
  7. [W] L.C. Washington, Introduction to cyclotomic fields. Springer-Verlag, New York, 1996. Zbl0966.11047MR1421575

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