Residue field domination
Appears in collection : Model theory of valued fields / Théorie des modèles des corps valués
The idea of stable domination for types in a theory was proposed and developed for algebraically closed valued fields in the eponymous book by Haskell, Hrushovski and Macpherson (2008). With the observation both that valued fields that are not algebraically closed generally have no stable part and that the stable part of an algebraically closed valued field is closely linked to the residue field, it seemed appropriate to consider a notion of residue field domination. In this talk, I will illustrate the idea of residue field domination with various examples, and then present some theorems which apply to some henselian valued fields of characteristic zero. These results are presented in a recent preprint of Ealy, Haskell and Simon, with similar results in a preprint of Vicaria.
