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An extension of Greenberg’s theorem to general valuation rings

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Abstract

We extend Greenberg’s strong approximation theorem to schemes of finite presentation over valuation rings with arbitrary value group. As an application, we prove a closed image theorem (in the strong topology on rational points) for proper morphisms of varieties over valued fields.

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Authors and Affiliations

  1. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France

    Laurent Moret-Bailly

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  1. Laurent Moret-Bailly
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Correspondence to Laurent Moret-Bailly.

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Dedicated to Jan Denef, on the occasion of his 60th birthday.

The author is a member of the ANR project “Points entiers et points rationnels”.

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Moret-Bailly, L. An extension of Greenberg’s theorem to general valuation rings. manuscripta math. 139, 153–166 (2012). https://doi.org/10.1007/s00229-011-0510-5

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  • DOI: https://doi.org/10.1007/s00229-011-0510-5

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