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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.

##### MSC:
 14G20 Local ground fields in algebraic geometry 14L05 Formal groups, $$p$$-divisible groups
##### Keywords:
formal geometry; Néron model; rigid geometry
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##### References:
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