| Résume | Motivated by work of Hrushovski on pseudofinite fields with an additive character, we introduce the theory ACFA+ which is the model companion of the theory of difference fields with an additive character on the fixed field. In this talk, we will present some basic properties of ACFA+ and see that it is given as the limit theory of the algebraic closure of finite fields with the standard character on the fixed field. Afterwards we will focus on type-amalgamation in ACFA+ and explain how 3-amalgamation already differs from the classical context in ACFA. If the time permits, we will explain how this reflects in model-theoretic Galois groups, notably the Kim-Pillay group. |
