A note on circular units in \(\mathbb Z_p\)-extensions.
type: Item
instance of: scholarly article
title: A note on circular units in \(\mathbb Z_p\)-extensions.
zbMATH Open document ID: 1097.11053
author: Radan Kučera
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2004-03-16T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/93883
review text: Since Kummer studied the arithmetic of the \(p\)-th cyclotomic field (\(p\) a fixed prime) and introduced the cyclotomic units, many authors (including Leopoldt, Gillard, Washington, Sinnott, Thaine ...) proposed different versions of ``circular units'' aiming at finding the best generalization to arbitrary abelian number fields. Too many versions, each with their own advantages, are provided. Kolster asked whether Sinnott's definition and Washington's definition would give the same Iwasawa module after the projective limit with respect to norms along \({\mathbb Z}_p\)-tower has been taken. A positive answer would have considerably eased the theory of Iwasawa descent for circular units. This paper provides a negative answer to this difficult question by describing explicit examples. Different examples have been independently given in a paper by the reviewer [Sous-modules d'unités en théorie d'Iwasawa. Publ. Math. UFR Sci. Tech. Besançon, Théorie des nombres, Années 1998/2001, 12 p. (2002; Zbl 1161.11394)].
reviewed by: Jean-Robert Belliard
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R27
zbMATH DE Number: 2058866
zbMATH Keywords: cyclotomic units
MaRDI profile type: Publication
OpenAlex ID: W2520994341
cites work: Q4205511
cites work: Cyclotomic units in \(\mathbb Z_p\)-extensions
cites work: A note on Thaine's circular units
cites work: Q3995821
cites work: On the Stickelberger ideal and the circular units of an abelian field
cites work: Q5690489
DOI: 10.5802/JTNB.399
description: scientific article; zbMATH DE number 2058866