Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-27T10:19:00.818Z Has data issue: false hasContentIssue false
  • English
  • Français

Special units and ideal class groups of extensions of imaginary quadratic fields

Published online by Cambridge University Press:  01 September 2007

BYUNGCHUL CHA
BYUNGCHUL CHA*
Affiliation:
Department of Mathematics and Computer Science, Hendrix College Conway, AR 72032, U.S.A. email: cha@hendrix.edu
Get access Rights & Permissions [Opens in a new window]

Extract

Let K be an imaginary quadratic field, and let F be an abelian extension of K, containing the Hilbert class field of K. We fix a rational prime p > 2 which does not divide the number of roots of unity in the Hilbert class field of K. Also, we assume that the prime p does not divide the order of the Galois group G:=Gal(F/K). Let AF be the ideal class group of F, and EF be the group of global units of F. The purpose of this paper is to study the Galois module structures of AF and EF.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 2 , September 2007 , pp. 265 - 270
Copyright
Copyright © Cambridge Philosophical Society 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Coleman, R.. On an archimedean characterization of the circular units. J. Reine Angew. Math. 356 (1985), 161–173.Google Scholar
[2]Rubin, K.. Global units and ideal class groups. Invent. Math. 89 (3) (1987), 511–526.Google Scholar
[3]Rubin, K.. The “main conjectures” of Iwasawa theory for imaginary quadratic fields. Invent. Math. 103 (1) (1991), 25–68.Google Scholar
[4]Seo, S.. Euler systems and special units. J. Number Theory. 109 (1) (2004), 59–68.Google Scholar
[5]Seo, S.. Truncated euler systems. Preprint, 2005.Google Scholar
[6]Sinnott, W.. On the stickelberger ideal and the circular units of a cyclotomic field. Annals Math. 108 (1978), 107–134.Google Scholar
[7]Thaine, F.. On the orders of ideal classes in prime cyclotomic fields. Math. Proc. Camb. Phil. Soc. 108 (2) (1990), 197–201.Google Scholar