On the Hermitian structure of the square root of the inverse different
type: Item
instance of: scholarly article
title: On the Hermitian structure of the square root of the inverse different
zbMATH Open document ID: 0789.11062
author: Christine Bachoc
publication date: 1994-06-13T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75014
review text: Let \(K\) be a number field which is Galois over \(\mathbb{Q}\), of odd degree and let \(G\) be its Galois group. There is a unique fractional ideal of \(K\) which is unimodular for the quadratic form \(\text{Trace}_{K/ \mathbb{Q}} (x^ 2)\). This ideal is the square root of the inverse different, and is denoted \(A_ K\). In this paper, we describe an explicit representative of the \(\mathbb{Z}[G]\)-isometry class of \((A_ K,\text{Trace}_{K/ \mathbb{Q}}(x^ 2))\), which depends only on the wildly ramified prime numbers \(p\) having a ramification index in \(K\) different from \(p\).
Mathematics Subject Classification ID: 11R33
Mathematics Subject Classification ID: 11E39
zbMATH DE Number: 490688
zbMATH Keywords: trace form
zbMATH Keywords: lattice
zbMATH Keywords: Hermitian module
zbMATH Keywords: explicit representative of \(\mathbb{Z}[G]\)-isometry class
zbMATH Keywords: inverse different
zbMATH Keywords: ramification index
MaRDI profile type: Publication
OpenAlex ID: W2335336037
cites work: Q3360951
cites work: Forme Trace et Ramification Sauvage
cites work: Réseaux unimodulaires
cites work: On the Galois structure of the square root of the codifferent
cites work: Q4039784
cites work: Q3808199
cites work: The Galois structure of the trace form in extensions of odd prime degree
cites work: Q5675788
cites work: Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers.
cites work: The ring of integers of an abelian number field.
cites work: Normal Bases in Galois Extensions of Number Fields
cites work: Q3856856
DOI: 10.5802/AIF.1350
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 490688