Néron models in the setting of formal and rigid geometry
type: Item
instance of: scholarly article
title: Néron models in the setting of formal and rigid geometry
zbMATH Open document ID: 0854.14011
DOI: 10.1007/BF01446633
author: Siegfried Bosch
author: Klaus Schlöter
published in: Mathematische Annalen
publication date: 1996-12-19T00:00:00Z
full work available at URL: https://eudml.org/doc/165295
review text: \(K\) is the field of fractions of a discrete and complete valuation ring \(R\). For a smooth \(K\)-scheme \(X\) one introduces the notion of Néron model. This notion is translated into terms of formal and rigid geometry over \(R\) and \(K\). A main result is the extension of Néron's existence theorem (of such a model) to the case where \(X\) is a rigid group such that the point set \(X_K(K^{sh})\) is bounded. Here \(K^{sh}\) denotes the field of fractions of the first henselization of \(R\). Also the relation between the Néron model of a finite type \(K\)-group scheme and the Néron model of the associated rigid \(K\)-group is studied. Some applications of this theory of Néron models of rigid groups are mentioned.
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 14L05
zbMATH DE Number: 734575
zbMATH Keywords: formal geometry
zbMATH Keywords: Néron model
zbMATH Keywords: rigid geometry
MaRDI profile type: Publication
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OpenAlex ID: W1994612386
description: scientific article; zbMATH DE number 734575