Submission date: 2 December 2020

Abstract:

We resolve the Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class there is an explicit 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.

Mathematics Subject Classification: 12L99, 14G25

Keywords and phrases:

Full text arXiv 2012.01307: pdf, ps.