Lang-Weil Type Estimates in Finite Difference Fields
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929371006107648 |
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| author | Hils, Martin Hrushovski, Ehud Ye, Jinhe Zou, Tingxiang |
| author_facet | Hils, Martin Hrushovski, Ehud Ye, Jinhe Zou, Tingxiang |
| contents | We prove a uniform estimate of the number of points for difference algebraic varieties in finite difference fields in the spirit of Lang-Weil. More precisely, we give uniform lower and upper bounds for the number of rational points of a difference variety in terms of its transformal dimension. As a main technical ingredient, we prove an equidimensionality result for Frobenius reductions of difference varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00880 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lang-Weil Type Estimates in Finite Difference Fields Hils, Martin Hrushovski, Ehud Ye, Jinhe Zou, Tingxiang Number Theory Algebraic Geometry Logic Primary 12H10, 11U09 Secondary 03C60, 03C20 We prove a uniform estimate of the number of points for difference algebraic varieties in finite difference fields in the spirit of Lang-Weil. More precisely, we give uniform lower and upper bounds for the number of rational points of a difference variety in terms of its transformal dimension. As a main technical ingredient, we prove an equidimensionality result for Frobenius reductions of difference varieties. |
| title | Lang-Weil Type Estimates in Finite Difference Fields |
| topic | Number Theory Algebraic Geometry Logic Primary 12H10, 11U09 Secondary 03C60, 03C20 |
| url | https://arxiv.org/abs/2406.00880 |