| Résume | Valuations arise as non-archimedean generalizations of absolute values, with examples coming from all over number theory and algebraic geometry. In many cases, henselian valuations turn out to be definable in the language of rings, a phenomenon famously observed (although perhaps not in these terms) by Julia Robinson in the context of the p-adics. In the late 2010s, Jahnke and Koenigsmann started a classification of when a henselian valuation is definable on a henselian field, providing a full characterization for the case where the so-called canonical henselian valuation has residue characteristic zero. We extend their work to the case where the residue characteristic is positive, drawing on the toolkit of independent defect to summon a definable henselian valuation out of certain defect extensions. This is joint work with Margarete Ketelsen (Münster) and Piotr Szewczyk (Dresden). |
