Open Access
October, 2012 The $l$-class group of the Z$_p$-extension over the rational field
Kuniaki HORIE, Mitsuko HORIE
J. Math. Soc. Japan 64(4): 1071-1089 (October, 2012). DOI: 10.2969/jmsj/06441071


Let $p$ be an odd prime, and let B$_\infty$ denote the Z$_p$-extension over the rational field. Let $l$ be an odd prime different from $p$. The question whether the $l$-class group of B$_\infty$ is trivial has been considered in our previous papers mainly for the case where $l$ varies with $p$ fixed. We give a criterion, for checking the triviality of the $l$-class group of B$_\infty$, which enables us to discuss the triviality when $p$ varies with $l$ fixed. As a consequence, we find that, if $l$ does not exceed 13 and $p$ does not exceed 101, then the $l$-class group of B$_\infty$ is trivial.


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Kuniaki HORIE. Mitsuko HORIE. "The $l$-class group of the Z$_p$-extension over the rational field." J. Math. Soc. Japan 64 (4) 1071 - 1089, October, 2012.


Published: October, 2012
First available in Project Euclid: 29 October 2012

zbMATH: 1234.11146
MathSciNet: MR2998917
Digital Object Identifier: 10.2969/jmsj/06441071

Primary: 11R29
Secondary: 11R20 , 11R23

Keywords: class number formula , Iwasawa theory , l-class group , reflection theorem , Zp-extension

Rights: Copyright © 2012 Mathematical Society of Japan

Vol.64 • No. 4 • October, 2012
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