Korean J. Math. Vol. 23 No. 3 (2015) pp.323-326
DOI: https://doi.org/10.11568/kjm.2015.23.3.323

On the anticyclotomic $\mathbb Z_{p}$-extension of an imaginary quadratic field

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Jangheon Oh


We prove that if a subfield of the Hilbert class field of an imaginary quadratic field $k$ meets the anticyclotomic ${\mathbb Z}_{p}$-extension $k_{\infty}^{a}$ of $k$, then it is contained in $k_{\infty}^{a}$ . And we give an example of an imaginay quadratic field $k$ with $\lambda_{3}(k_{\infty}^{a}) \geq 8.$

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