Rational points of rigid-analytic sets: a Pila-Wilkie type theorem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913896680390656 |
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| author | Binyamini, Gal Kato, Fumiharu |
| author_facet | Binyamini, Gal Kato, Fumiharu |
| contents | We establish a rigid-analytic analog of the Pila-Wilkie counting theorem, giving sub-polynomial upper bounds for the number of rational points in the transcendental part of a $\mathbb{Q}_p$-analytic set, and the number of rational functions in a $\mathbb{F}_q((t))$-analytic set. For $\mathbb{Z}[[t]]$-analytic sets we prove such bounds uniformly for the specialization to every non-archimedean local field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_10530 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rational points of rigid-analytic sets: a Pila-Wilkie type theorem Binyamini, Gal Kato, Fumiharu Number Theory Algebraic Geometry Logic We establish a rigid-analytic analog of the Pila-Wilkie counting theorem, giving sub-polynomial upper bounds for the number of rational points in the transcendental part of a $\mathbb{Q}_p$-analytic set, and the number of rational functions in a $\mathbb{F}_q((t))$-analytic set. For $\mathbb{Z}[[t]]$-analytic sets we prove such bounds uniformly for the specialization to every non-archimedean local field. |
| title | Rational points of rigid-analytic sets: a Pila-Wilkie type theorem |
| topic | Number Theory Algebraic Geometry Logic |
| url | https://arxiv.org/abs/2203.10530 |