Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON THE ANTICYCLOTOMIC ℤp-EXTENSION OF AN IMAGINARY QUADRATIC FIELD

  • OH, JANGHEON (Faculty of Mathematics and Statistics Sejong University)
  • Received : 2015.04.09
  • Accepted : 2015.07.08
  • Published : 2015.09.30
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Abstract

We prove that if a subfield of the Hilbert class field of an imaginary quadratic field k meets the anticyclotomic $\mathbb{Z}_p$-extension $k^a_{\infty}$ of k, then it is contained in $k^a_{\infty}$. And we give an example of an imaginay quadratic field k with ${\lambda}_3(k^a_{\infty}){\geq}8$.

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References

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