Improved Lang--Weil bounds for a geometrically irreducible hypersurface over a finite field
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866929368206409728 |
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| author | Slavov, Kaloyan |
| author_facet | Slavov, Kaloyan |
| contents | We sharpen to nearly optimal the known asymptotic and explicit bounds for the number of $\mathbb{F}_q$-rational points on a geometrically irreducible hypersurface over a (large) finite field. The proof involves a Bertini-type probabilistic combinatorial technique. Namely, we study the number of $\mathbb{F}_q$-points on the intersection of the given hypersurface with a random plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_14868 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Improved Lang--Weil bounds for a geometrically irreducible hypersurface over a finite field Slavov, Kaloyan Algebraic Geometry 14G15, 11T06, 14G05, 05B25 We sharpen to nearly optimal the known asymptotic and explicit bounds for the number of $\mathbb{F}_q$-rational points on a geometrically irreducible hypersurface over a (large) finite field. The proof involves a Bertini-type probabilistic combinatorial technique. Namely, we study the number of $\mathbb{F}_q$-points on the intersection of the given hypersurface with a random plane. |
| title | Improved Lang--Weil bounds for a geometrically irreducible hypersurface over a finite field |
| topic | Algebraic Geometry 14G15, 11T06, 14G05, 05B25 |
| url | https://arxiv.org/abs/2105.14868 |