Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the first layer of anti-cyclotomic $\mathbf {Z}_{p}$-extension of imaginary quadratic fields

Jangheon Oh

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Abstract

In this paper, we give an explicit description of the first layer of anti-cyclotomic $\mathbf{Z}_{p}$-extension of imaginary quadratic fields.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 83, Number 3 (2007), 19-20.

Dates
First available in Project Euclid: 9 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1176126884

Digital Object Identifier
doi:10.3792/pjaa.83.19

Mathematical Reviews number (MathSciNet)
MR2317304

Zentralblatt MATH identifier
1123.11032

Subjects
Primary: 11R23: Iwasawa theory

Keywords
Iwasawa theory anti-cyclotomic extension Kunner extension Minkowski unit

Citation

Oh, Jangheon. On the first layer of anti-cyclotomic $\mathbf {Z}_{p}$-extension of imaginary quadratic fields. Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 3, 19--20. doi:10.3792/pjaa.83.19. https://projecteuclid.org/euclid.pja/1176126884


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References

  • H. Cohen, Advanced Topics in Computational Number Theory, Springer, New York, 2000.
  • J. M. Kim and J. Oh, Defining Polynomial of the first layer of anti-cyclotomic $\mathbf{Z}_{3}$-extension of imaginary quadratic fields of class number 1, Proc.Japan Acad. Ser.A Math. Sci. 80 (2004), no. 3, 18–19.
  • J. Oh, The first layer of $\mathbf{Z}_{2}^2$-extension over imaginary quadratic fields, Proc. Japan Acad. Ser.A Math. Sci. 76 (2000), no. 9, 132–134.
  • L. C. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982.