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arXiv · 2104.04339

Incidence bounds in positive characteristic via valuations and distality

Martin Bays·Jean-François Martin
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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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Martin Bays, Jean-François Martin. 2026-04-14. Incidence bounds in positive characteristic via valuations and distality. https://doi.org/10.5802/ahl.174

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