On a relative normal integral basis problem over abelian number fields
type: Item
instance of: scholarly article
title: On a relative normal integral basis problem over abelian number fields
zbMATH Open document ID: 0806.11050
author: Humio Ichimura
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-08-08T00:00:00Z
review text: This is an announcement of the following result. Let \(p\) be a fixed odd prime number, let \(K\) be a number field containing the \(p\)-th roots of unity and let \(C_ p\) be a cyclic group of order \(p\). In this paper the quotient is considered of the group of all realizations of \(C_ p\) as a Galois group over \(K\) and the subgroup of those realizations which have a relative normal integral basis. A description, in terms of power series attached to \(p\)-adic \(L\)- functions, is given of the Galois module structure of this quotient when \(K\) runs over all layers of the cyclotomic \(\mathbb{Z}_ p\)-extensions of a certain imaginary abelian field.
Mathematics Subject Classification ID: 11R33
Mathematics Subject Classification ID: 11R20
zbMATH DE Number: 597333
zbMATH Keywords: relative normal integral basis
zbMATH Keywords: \(p\)-adic \(L\)-functions
zbMATH Keywords: Galois module structure
zbMATH Keywords: imaginary abelian field
reviewed by: J. Brinkhuis
MaRDI profile type: Publication
full work available at URL: pjaa.69.413
OpenAlex ID: W2038216206
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DOI: 10.3792/PJAA.69.413
description: scientific article; zbMATH DE number 597333