| Résume | A core question in the model theory of fields is to understand how combinatorial patterns and algebraic properties interact. An example of that is a well-known result by Kaplan, Scanlon and Wagner, which states that infinite NIP fields of characteristic p have no Artin-Schreier extension. This result has since then been proven by Hempel to also hold for NIPn fields, and a weaker version has been obtained by Chernikov, Kaplan and Simon for NTP2 fields. In this talk, we will study this result and formulate it in terms of explicit formulas, allowing us to lift complexity from the residue field, and obtain a partial classification of NIPn henselian valued fields. |
