An extension of Greenberg's theorem to general valuation rings

Details An extension of Greenberg's theorem to general valuation rings An extension of Greenberg's theorem to general valuation rings

2011-06-06

arxiv.org/abs/1106.0984v3

Mathematics

Algebraic Geometry

15 pages, dedicated to Jan Denef; Manuscripta mathematica, 2011. The final article is avaliable at springerlink.com: http://

Scientific paper

10.1007/s00229-011-0510-5

We extend Greenberg's strong approximation theorem to schemes of finite
presentation over valuation rings with arbitrary value group, using the
ultraproduct method of Becker, Denef, Lipshitz and van den Dries. 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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