English

Characterizing finitely generated fields by a single field axiom

Logic 2023-11-02 v2 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.2012.01307,
  title  = {Characterizing finitely generated fields by a single field axiom},
  author = {Philip Dittmann and Florian Pop},
  journal= {arXiv preprint arXiv:2012.01307},
  year   = {2023}
}

Comments

final version

R2 v1 2026-06-23T20:40:36.359Z