| Résume | The pseudo-algebraically closed (PAC), pseudo real closed (PRC), and pseudo p-adically closed fields (PpC) are examples of unstable fields that have similarities, but have often been studied separately. In this talk, we propose a unified framework for studying these fields - the class of pseudo-T-closed fields, where T is an enriched theory of field. These fields verify a "local-global" principle for the existence of points on varieties based on models of T. This approach also enables a good description of some fields equipped with multiple V-topologies, particularly pseudo-algebraically closed fields with a finite number of V-topologies.
One important result is a (model theoretic) classification result for bounded pseudo-T-closed fields, in particular we can show that under specific hypotheses in T, these fields are NTP2.
This is joint work with Silvain Rideau-Kikuchi |
