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Néron models in the setting of formal and rigid geometry. (English) Zbl 0854.14011
\(K\) 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.

14G20 Local ground fields in algebraic geometry
14L05 Formal groups, \(p\)-divisible groups
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