BGU Seminar in Logic, Set Theory and Topology.

BGU Seminar in Logic, Set Theory and Topology.

Title: Generically Stable Varieties and Groups in ACVF

Abstract:

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.