Tohoku Mathematical Journal
2005
September
SECOND SERIES VOL. 57, NO. 3

Tohoku Math. J.
57 (2005), 375-394

Title THE IDEAL CLASS GROUP OF THE BASIC $\boldsymbol{Z}_p$-EXTENSION OVER AN IMAGINARY QUADRATIC FIELD

Author Kuniaki Horie

(Received October 14, 2003, revised November 15, 2004)
Abstract. We shall discuss the local triviality in the ideal class group of the basic $\boldsymbol{Z}_p$-extension over an imaginary quadratic field and prove, in particular, a result which implies that such triviality distributes with natural density 1.

2000 Mathematics Subject Classification. Primary 11R29; Secondary 11R11, 11R20, 11R23.

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