Galois module structure of Kummer orders and elliptic units
type: Item
instance of: scholarly article
title: Galois module structure of Kummer orders and elliptic units
zbMATH Open document ID: 0819.11053
DOI: 10.1007/BF02567708
published in: Manuscripta Mathematica
publication date: 1995-08-31T00:00:00Z
full work available at URL: https://eudml.org/doc/155938
review text: Let \(K\) be a quadratic imaginary number field. Let \(f\) denote a rational integer which is coprime to 6. Let \(K(f^ 2)\) (resp. \(K(f)\)) denote the ray class field of \(K\) of conductor \(f^ 2\) (resp. \(f\)). Let \(\Gamma\) denote the Galois group of \(K(f^ 2)/ K(f)\) and let \({\mathfrak M}\) denote the unique maximal order of \(K(f)\Gamma\). It is shown that the Kummer order \(\widetilde {\mathcal O}_{K(f^ 2)}= \{\alpha\in K(f^ 2)\mid \alpha{\mathfrak M}\subseteq {\mathcal O}_{K(f^ 2)}\}\) is a free, rank one \({\mathfrak M}\)-module. An explicit generator is given by singular values of certain modular functions.
Mathematics Subject Classification ID: 11R33
Mathematics Subject Classification ID: 11G16
zbMATH DE Number: 572234
zbMATH Keywords: Galois module
zbMATH Keywords: elliptic units
zbMATH Keywords: ray class field
zbMATH Keywords: Kummer order
zbMATH Keywords: explicit generator
author: Werner Bley
reviewed by: J. Brinkhuis
MaRDI profile type: Publication
cites work: Q3758001
cites work: The module structure of Kummer extensions over Dedekind domains.
cites work: Some applications of Kronecker's limit formulas
cites work: Galoismodulstruktur und elliptische Funktionen. (Galois module structure and elliptic functions)
OpenAlex ID: W2003244220
description: scientific article; zbMATH DE number 572234