Translator Disclaimer
June 2020 On the Structure of the Galois Group of the Maximal Pro-$p$ Extension with Restricted Ramification over the Cyclotomic $\mathbb{Z}_p$-extension
Tsuyoshi ITOH
Tokyo J. Math. 43(1): 181-204 (June 2020). DOI: 10.3836/tjm/1502179301

Abstract

Let $k_\infty$ be the cyclotomic $\mathbb{Z}_p$-extension of an algebraic number field $k$. We denote by $S$ a finite set of prime numbers which does not contain $p$, and $S(k_\infty)$ the set of primes of $k_\infty$ lying above $S$. In the present paper, we will study the structure of the Galois group $\mathcal{X}_S (k_\infty)$ of the maximal pro-$p$ extension unramified outside $S (k_\infty)$ over $k_\infty$. We mainly consider the question whether $\mathcal{X}_S (k_\infty)$ is a non-abelian free pro-$p$ group or not. In the former part, we treat the case when $k$ is an imaginary quadratic field and $S = \emptyset$ (here $p$ is an odd prime number which does not split in $k$). In the latter part, we treat the case when $k$ is a totally real field and $S \neq \emptyset$.

Citation

Download Citation

Tsuyoshi ITOH. "On the Structure of the Galois Group of the Maximal Pro-$p$ Extension with Restricted Ramification over the Cyclotomic $\mathbb{Z}_p$-extension." Tokyo J. Math. 43 (1) 181 - 204, June 2020. https://doi.org/10.3836/tjm/1502179301

Information

Published: June 2020
First available in Project Euclid: 24 August 2019

zbMATH: 07227185
MathSciNet: MR4121793
Digital Object Identifier: 10.3836/tjm/1502179301

Subjects:
Primary: 11R23

Rights: Copyright © 2020 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
24 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.43 • No. 1 • June 2020
Back to Top