Different groups of circular units of a compositum of real quadratic fields

• Autorzy: Radan Kučera
• Języki publikacji: EN

Abstrakty

EN

There are many different definitions of the group of circular units of a real abelian field. The aim of this paper is to study their relations in the special case of a compositum k of real quadratic fields such that -1 is not a square in the genus field K of k in the narrow sense.
The reason why fields of this type are considered is as follows. In such a field it is possible to define a group C of units (slightly bigger than Sinnott's group of circular units) such that the Galois group acts on C/(±C²) trivially (see [K, Lemma 2]).
Due to this key property we can easily compare different groups of circular units (see the conclusion of this paper).

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1994
• Tom: 67
• Numer: 2
• Strony: 123-140

Daty

wydano

1994

otrzymano

1993-03-17

Twórcy

autor

Radan Kučera

• Department of Mathematics, Masaryk University, Janáčkovo Nám. 2a, 662 95 Brno, Czech Republic

Bibliografia

• [G] R. Gillard, Remarques sur les unités cyclotomiques et les unités elliptiques, J. Number Theory 11 (1979), 21-48.
• [K] R. Kučera, On the Stickelberger ideal and circular units of a compositum of quadratic fields, preprint.
• [L] G. Lettl, A note on Thaine's circular units, J. Number Theory 35 (1990), 224-226.
• [S] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234.
• [W] L. C. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982.