Tohoku Mathematical Journal

The ideal class group of the $\boldsymbol{Z}_p$-extension over the rationals

Kuniaki Horie and Mitsuko Horie

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Abstract

For any prime number $p$, we study local triviality of the ideal class group of the ${\boldsymbol Z}_p$-extension over the rational field. We improve a known general result in such study by modifying the proof of the result, and pursue known effective arguments on the above triviality with the help of a computer. Some explicit consequences of our investigations are then provided in the case $p\leq7$.

Article information

Source
Tohoku Math. J. (2), Volume 61, Number 4 (2009), 551-570.

Dates
First available in Project Euclid: 21 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1264084499

Digital Object Identifier
doi:10.2748/tmj/1264084499

Mathematical Reviews number (MathSciNet)
MR2598249

Zentralblatt MATH identifier
1238.11101

Subjects
Primary: 11R29: Class numbers, class groups, discriminants
Secondary: 11R18: Cyclotomic extensions 11R20: Other abelian and metabelian extensions 11R23: Iwasawa theory

Keywords
Ideal class group boldsymbol Z}_p$-extension

Citation

Horie, Kuniaki; Horie, Mitsuko. The ideal class group of the $\boldsymbol{Z}_p$-extension over the rationals. Tohoku Math. J. (2) 61 (2009), no. 4, 551--570. doi:10.2748/tmj/1264084499. https://projecteuclid.org/euclid.tmj/1264084499


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References

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