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Preprint Number 1121

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1121. Yatir Halevi
On Stably Pointed Varieties and Generically Stable Groups in ACVF

Submission date: 16 November 2016


We give a geometric description of the pair (V,p), where V is an algebraic variety over a valued field F with valuation ring O_F and p is a Zariski dense generically stable type concentrated on V, by defining a fully faithful functor to the category of schemes over O_F with residual dominant morphisms over O_F.
Under this functor, an algebraic group and a generically stable generic of a subgroup gets sent to a group scheme over O_F. This returns a geometric description of the subgroup as the set of O_F-points of the group scheme, generalizing a previous result in the affine case.
We also study a maximum modulus principle on schemes over O_F and show that the schemes obtained by this functor enjoy it.

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Full text arXiv 1611.05422: pdf, ps.

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