Incidence bounds in positive characteristic via valuations and distality
Logic
2026-04-15 v4 Combinatorics
Abstract
We prove distality of quantifier-free relations on valued fields with finite residue field. By a result of Chernikov-Galvin-Starchenko, this yields Szemer\'edi-Trotter-like incidence bounds for function fields over finite fields. We deduce a version of the Elekes-Szab\'o theorem for such fields.
Keywords
Cite
@article{arxiv.2104.04339,
title = {Incidence bounds in positive characteristic via valuations and distality},
author = {Martin Bays and Jean-François Martin},
journal= {arXiv preprint arXiv:2104.04339},
year = {2026}
}
Comments
v2: local fixes; v3: local clarifications (published version); v4: fix minor error with parameters in defn of "distal in"