Volume 6 (2023)
Bays, Martin; Martin, Jean-François
Incidence bounds in positive characteristic via valuations and distality
Annales Henri Lebesgue, Volume 6 (2023), pp. 627-641.

Metadata

DOI10.5802/ahl.174
Keywords Szemerédi-Trotter, incidence bounds, distality, Elekes-Szabó

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.


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