A note on circular units in ℤ p -extensions
Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 223-229.

Nous nous intéressons aux limites projectives des groupes de Sinnott et des groupes de Washington des unités circulaires dans la ℤ p -extension d’un corps abélien. Nous montrons par un exemple qu’en général ces deux limites ne coïncident pas.

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.

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     title = {A note on circular units in $\mathbb {Z}_p$-extensions},
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     publisher = {Universit\'e Bordeaux I},
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Radan Kučera. A note on circular units in $\mathbb {Z}_p$-extensions. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 223-229. https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_223_0/

[B] J.-R. Belliard, Sous-modules d'unités en théorie d'Iwasawa, to appear in Publications mathématiques de l'Université de Franche-Comté. | MR

[GK] R. Gold, J. Kim, Bases for cyclotomic units. Compositio Math. 71 (1989), 13-27. | Numdam | MR | Zbl

[KN] R. Kučera, J. Nekovář, Cyclotomic units in Zp-extensions. J. Algebra 171 (1995), 457-472. | MR | Zbl

[L] G. Lettl, A note on Thaine's circular units. J. Number Theory 35 (1970), 224-226. | MR | Zbl

[R] K. Rubin, The main conjecture, appendix in S. Lang, Cyclotomic Fields I and II, Springer-Verlag, New York, 1990. | MR | Zbl

[S] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field. Invent. Math. 62 (1980), 181-234. | MR | Zbl

[W] L.C. Washington, Introduction to cyclotomic fields. Springer-Verlag, New York, 1996. | MR | Zbl