Proceedings of the Japan Academy, Series A, Mathematical Sciences

Notes on the structure of the ideal class groups of abelian number fields

Miho Aoki

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Abstract

In this paper, we give explicit formulae of certain higher annihilators of the ideal class groups defined by V. Kolyvagin and K. Rubin, which come from Euler systems of Stickelberger elements and cyclotomic units. Further, using these explicit formulae, we reformulate Kolyvagin-Rubin's structure theorem of the ideal class groups of abelian number fields.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 5 (2005), 69-74.

Dates
First available in Project Euclid: 3 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1117805144

Digital Object Identifier
doi:10.3792/pjaa.81.69

Mathematical Reviews number (MathSciNet)
MR2143545

Zentralblatt MATH identifier
1084.11060

Subjects
Primary: 11R23: Iwasawa theory
Secondary: 11R18: Cyclotomic extensions 11R29: Class numbers, class groups, discriminants

Keywords
Ideal class groups Euler systems

Citation

Aoki, Miho. Notes on the structure of the ideal class groups of abelian number fields. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 5, 69--74. doi:10.3792/pjaa.81.69. https://projecteuclid.org/euclid.pja/1117805144


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References

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