Submission date: 9 April 2021

Abstract:

We prove distality of quantifier-free relations on valued fields with finite residue field. By a result of Chernikov-Galvin-Starchenko, this yields Szemerédi-Trotter-like incidence bounds for function fields over finite fields. We deduce a version of the Elekes-Szabó theorem for such fields.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2104.04339: pdf, ps.