Rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915998010966016 |
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| author | Aubry, Yves Voloch, José Felipe |
| author_facet | Aubry, Yves Voloch, José Felipe |
| contents | We improve a bound due to the second author on number of rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields and look at families of surfaces that achieve or nearly achieve this bound, for which we compute their exact number of rational points. These computations may have independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09166 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields Aubry, Yves Voloch, José Felipe Number Theory Algebraic Geometry 11G25, 14G15 We improve a bound due to the second author on number of rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields and look at families of surfaces that achieve or nearly achieve this bound, for which we compute their exact number of rational points. These computations may have independent interest. |
| title | Rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields |
| topic | Number Theory Algebraic Geometry 11G25, 14G15 |
| url | https://arxiv.org/abs/2605.09166 |