Characterizing finitely generated fields by a single field axiom


We resolve the strong Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class there is a first-order sentence which characterizes this field within the class up to isomorphism. Our solution is conditional on resolution of singularities in characteristic two and unconditional in all other characteristics.


Philip Dittmann

Technische Universität Dresden, Fachringtung Mathematik, Institut für Algebra, Dresden, Germany

Florian Pop

Department of Mathematics, University of Pennsylvania, Philadelphia, PA, USA