Decomposition and inertia groups in \({\mathbb{Z}}_ p\)-extensions
type: Item
instance of: scholarly article
title: Decomposition and inertia groups in \({\mathbb{Z}}_ p\)-extensions
zbMATH Open document ID: 0606.12003
author: Georges Gras
published in: Tokyo Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The author gives a description of the decomposition, inertia, and higher ramification groups in a \({\mathbb{Z}}_ p\)-extension of a number field k. This is accomplished via a logarithm function [the author, J. Reine Angew. Math. 343, 64-80 (1983; Zbl 0501.12015)] which gives a canonical isomorphism between the Galois group of the compositum of all \({\mathbb{Z}}_ p\)-extensions of k and a certain \({\mathbb{Z}}_ p\)-module attached to k. The case of imaginary quadratic fields is worked out in detail.
reviewed by: Lawrence C. Washington
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11S15
zbMATH DE Number: 3979186
zbMATH Keywords: decomposition groups
zbMATH Keywords: Iwasawa theory
zbMATH Keywords: higher ramification groups
zbMATH Keywords: logarithm function
zbMATH Keywords: \({bbfZ}_ p\)-extensions
zbMATH Keywords: imaginary quadratic fields
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270150974
OpenAlex ID: W2060870013
DOI: 10.3836/TJM/1270150974
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description: scientific article; zbMATH DE number 3979186