Tohoku Mathematical Journal

The ideal class group of the basic $\mathbf Z_p$-extension over an imaginary quadratic field

Kuniaki Horie

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Abstract

We shall discuss the local triviality in the ideal class group of the basic $\mathbf Z_p$-extension over an imaginary quadratic field and prove, in particular, a result which implies that such triviality distributes with natural density $1$.

Article information

Source
Tohoku Math. J. (2), Volume 57, Number 3 (2005), 375-394.

Dates
First available in Project Euclid: 7 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1128703003

Digital Object Identifier
doi:10.2748/tmj/1128703003

Mathematical Reviews number (MathSciNet)
MR2154097

Zentralblatt MATH identifier
1128.11051

Subjects
Primary: 11R29: Class numbers, class groups, discriminants
Secondary: 11R11: Quadratic extensions 11R20: Other abelian and metabelian extensions 11R23: Iwasawa theory

Citation

Horie, Kuniaki. The ideal class group of the basic $\mathbf Z_p$-extension over an imaginary quadratic field. Tohoku Math. J. (2) 57 (2005), no. 3, 375--394. doi:10.2748/tmj/1128703003. https://projecteuclid.org/euclid.tmj/1128703003


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References

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