A note on circular units in \(\mathbb Z_p\)-extensions.
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)].
scientific article; zbMATH DE number 2058866