Completion of r. t. extensions of local fields. II
type: Item
instance of: scholarly article
title: Completion of r. t. extensions of local fields. II
zbMATH Open document ID: 0923.12010
author: N. Popescu
author: V. Alexandru
author: Angel Popescu
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1999-05-18T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108463
review text: Let \((K,v)\) be a local field. An extension \(w\) of \(v\) to \(K(X)\) is called residual transcendental (r.t.-extension) if the residue field of \(w\) is a transcendental extension of the residual field of \(v\). In the first part of this paper [Math. Z. 221, 675-682 (1996; Zbl 0852.12003)] the authors described the completion \((\widetilde{K(X)},\widetilde w)\) of \((K(X),w) \), where \(w\) is the Gauss r.t.-extension of \(v\). In this paper they consider the general case of any r.t.-extension of \(v\). For the description of elements of the completion they use the embedding of \((K(X),w)\) into the valued field \(K' \{\{X-a.\delta\}\}\) of \(\delta\)-formal Laurent series over the local field \((K', v')\), where \(\delta\) is an appropriate rational number, and \(K'=K(a) \subset \overline K\), \(a\in\overline K\) (the algebraic closure of \(K)\). Moreover, they describe \((\widetilde{K(X)},\widetilde w)\) as a finite extension of \((\widetilde {K(r)}, \widetilde{w_0})\), where \(r\in K(X)\) and \(w_0\) is the Gauss r.t.-extension of \(v\).
Mathematics Subject Classification ID: 12J10
Mathematics Subject Classification ID: 12F99
Mathematics Subject Classification ID: 12J20
zbMATH DE Number: 1279128
zbMATH Keywords: residual transcendental extension
zbMATH Keywords: local field
reviewed by: Jiří Močkoř
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1279128