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

Jangheon Oh

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 $k_{\infty}^{a}$ of $k$, then it is contained in  $k_{\infty}^{a}$ . And we give an example of an imaginay quadratic field $k$ with  $\lambda_{3}(k_{\infty}^{a}) \geq 8.$

Keywords


Iwasawa theory, anticylotomic extension, Hilbert class field.

Subject classification

11R23.

Sponsor(s)



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References


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