Submission date: 22 October 2018

Abstract:

We give a construction of a family of definable subrings of finitely generated fields K of characteristic not two. We deduce that for any such K there exists a first-order sentence φ_K characterising K in the class of finitely generated fields, i.e. such that for any finitely generated field L we have L ⊧ φ_K if and only if L ≡ K. This answers a question considered by Pop and others, at least when the characteristic is not two. Our method is similar to previous approaches to the question, using Pfister forms and a local-global principle in cohomology.

Mathematics Subject Classification: 12L99, 14G25

Keywords and phrases:

Full text arXiv 1810.09333: pdf, ps.