Incidence bounds in positive characteristic via valuations and distality
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866913030344802304 |
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| author | Bays, Martin Martin, Jean-François |
| author_facet | Bays, Martin Martin, Jean-François |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_04339 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Incidence bounds in positive characteristic via valuations and distality Bays, Martin Martin, Jean-François Logic Combinatorics 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. |
| title | Incidence bounds in positive characteristic via valuations and distality |
| topic | Logic Combinatorics |
| url | https://arxiv.org/abs/2104.04339 |