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A NOTE ON THE FIRST LAYERS OF ℤp-EXTENSIONS

Oh, Jang-Heon

  • Published : 2009.01.31

Abstract

In this paper we explicitly compute a Minkowski unit of a real abelian field and give a criterion when the first layer of anti-cyclotomic ${\mathbb{Z}}_3$-extension of an imaginary quadratic field is unramified everywhere.

Keywords

Minkowski unit;anti-cyclotomic extension;${\mathbb{Z}}_p$-extension

References

  1. J. Minardi, Iwasawa modules for $Z_p^d$-extensions of algebraic number fields, Ph. D. dissertation, University of Washington, 1986.
  2. J. Oh, Defining Polynomial of the first layer of anti-cyclotomic $\mathbb{Z}_3$-extension of imaginary quadratic fields of class number 1, Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 3, 18-19. https://doi.org/10.3792/pjaa.80.18
  3. J. Oh, The first layer of $\mathbb{Z}^2_2$-extension over imaginary quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 9, 132-134. https://doi.org/10.3792/pjaa.76.132
  4. J. Oh, , On the first layer of anti-cyclotomic $\mathbb{Z}_p$-extension of imaginary quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 3, 19-20. https://doi.org/10.3792/pjaa.83.19
  5. L. Washington, Introduction to Cyclotomic Fields, Graduate Text in Math. Vol. 83, Springer-Verlag, 1982.

Cited by

  1. CONSTRUCTION OF THE FIRST LAYER OF ANTI-CYCLOTOMIC EXTENSION vol.21, pp.3, 2013, https://doi.org/10.11568/kjm.2013.21.3.265
  2. ON THE ANTICYCLOTOMIC ℤp-EXTENSION OF AN IMAGINARY QUADRATIC FIELD vol.23, pp.3, 2015, https://doi.org/10.11568/kjm.2015.23.3.323
  3. ANTI-CYCLOTOMIC EXTENSION AND HILBERT CLASS FIELD vol.25, pp.1, 2012, https://doi.org/10.14403/jcms.2012.25.1.091