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April 2014 On tamely ramified Iwasawa modules for the cyclotomic $\mathbb {Z}_{p}$-extension of abelian fields
Tsuyoshi Itoh
Osaka J. Math. 51(2): 513-537 (April 2014).

Abstract

Let $p$ be an odd prime, and $k_{\infty}$ the cyclotomic $\mathbb{Z}_{p}$-extension of an abelian field $k$. For a finite set $S$ of rational primes which does not include $p$, we will consider the maximal $S$-ramified abelian pro-$p$ extension $M_{S} (k_{\infty})$ over $k_{\infty}$. We shall give a formula of the $\mathbb{Z}_{p}$-rank of $\mathrm{Gal}(M_{S} (k_{\infty})/k_{\infty})$. In the proof of this formula, we also show that $M_{\{q\}} (k_{\infty})/L(k_{\infty})$ is a finite extension for every real abelian field $k$ and every rational prime $q$ distinct from $p$, where $L(k_{\infty})$ is the maximal unramified abelian pro-$p$ extension over $k_{\infty}$.

Citation

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Tsuyoshi Itoh. "On tamely ramified Iwasawa modules for the cyclotomic $\mathbb {Z}_{p}$-extension of abelian fields." Osaka J. Math. 51 (2) 513 - 537, April 2014.

Information

Published: April 2014
First available in Project Euclid: 8 April 2014

zbMATH: 1300.11111
MathSciNet: MR3192553

Subjects:
Primary: 11R23
Secondary: 11R18

Rights: Copyright © 2014 Osaka University and Osaka City University, Departments of Mathematics

JOURNAL ARTICLE
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Vol.51 • No. 2 • April 2014
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