Generically Stable Varieties and Groups in ACVF

Generically stable groups and more specifically algebraic groups with generically stable generics were studied by Hrushovski in ”Valued fields, Metastable Groups“. We‘ll talk about a class of group schemes over the valuation ring definable in ACVF and show that they are generically stable. In fact, we define a functor between the category of algebraic varieties with a Zariski dense generically stable type concentrated on it to generically stable definable schemes over the valuation ring. If everything is over a model, algebraic groups get sent to group schemes. If time permits we may say a few words about strongly stably dominated types.