We give a geometric description of the pair (V, p), where V is an algebraic variety over a valued field F with valuation ring $\mathcal{O}_F$ and p is a Zariski dense generically stable type concentrated on V, by defining a fully faithful functor to the category of schemes over $\mathcal{O}_F$ with residual dominant morphisms over $\mathcal{O}_F$ .
Under this functor, the pair (an algebraic group, a generically stable generic type of a subgroup) gets sent to a group scheme over $\mathcal{O}_F$ .
This returns a geometric description of the subgroup as the set of $\mathcal{O}_F$ -points of the group scheme, generalizing a previous result in the affine case by Hrushovski. If time permits we may say a few words about strongly stably dominated types.