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Preprint Number 1963

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1963. Martin Bays and Jean-François Martin
Incidence bounds in positive characteristic via valuations and distality

Submission date: 9 April 2021


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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Full text arXiv 2104.04339: pdf, ps.

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