Maximum number of rational points on hypersurfaces in weighted projective spaces over finite fields
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912744378204160 |
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| author | Aubry, Yves Perret, Marc |
| author_facet | Aubry, Yves Perret, Marc |
| contents | An upper bound for the maximum number of rational points on an hypersurface in a projective space over a finite field has been conjectured by Tsfasman and proved by Serre in 1989. The analogue question for hypersurfaces on weighted projective spaces has been considered by Castryck, Ghorpade, Lachaud, O'Sullivan, Ram and the first author in 2017. A conjecture has been proposed there and proved in the particular case of the dimension 2. We prove here the conjecture in any dimension provided the second weight is also equal to one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07522 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximum number of rational points on hypersurfaces in weighted projective spaces over finite fields Aubry, Yves Perret, Marc Algebraic Geometry An upper bound for the maximum number of rational points on an hypersurface in a projective space over a finite field has been conjectured by Tsfasman and proved by Serre in 1989. The analogue question for hypersurfaces on weighted projective spaces has been considered by Castryck, Ghorpade, Lachaud, O'Sullivan, Ram and the first author in 2017. A conjecture has been proposed there and proved in the particular case of the dimension 2. We prove here the conjecture in any dimension provided the second weight is also equal to one. |
| title | Maximum number of rational points on hypersurfaces in weighted projective spaces over finite fields |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2402.07522 |