Résume | The Ax-Kochen/Ersov theorem is a classic result in the model theory of valued fields. It can be paraphrased as saying that the elementary theory of a valued field is determined by the theory of the value group and the theory of the residue field. At the level of types, the intuition is that a type should be controlled by its trace in each of the residue field and value group. In this talk, I will explore some ways in which this intuition can be made precise, and also some limitations to that preliminary intuition. I will try to give lots of examples to keep the discussion concrete. |