Models of elliptic curves, using model theory

Given a valued field (K,v) with valuation ring O and an algebraic group G over K, a model of G is a group scheme \mathcal{G} over O for which \mathcal{G}\times_O K=G. We exhibit the existence of such models for G an elliptic curve and K an algebraically closed field and on the way we classify the different group schemes one can get. The proof uses a combination of tools from model theory and algebraic geometry.

The aim of this talk is to state the theorem and to introduce some of the model theoretic notions required for the proof.

No prior knowledge in model theory is required, though a basic course in logic will help.