Weil conjectures and affine hypersurfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912854139994112 |
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| author | Zhang, Dingxin |
| author_facet | Zhang, Dingxin |
| contents | We give yet another proof of the Riemann hypothesis for smooth projective varieties over a finite field (Deligne's theorem), by reducing to the hypersurface case. The latter was established by N. Katz via an elementary argument. A reduction of this kind was previously carried out by A. J. Scholl. Our approach is slightly different, and relies on deformation to an affine hypersurface, together with Artin's vanishing theorem and basic properties of perverse sheaves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20187 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weil conjectures and affine hypersurfaces Zhang, Dingxin Algebraic Geometry Number Theory 11G25, 14G15 We give yet another proof of the Riemann hypothesis for smooth projective varieties over a finite field (Deligne's theorem), by reducing to the hypersurface case. The latter was established by N. Katz via an elementary argument. A reduction of this kind was previously carried out by A. J. Scholl. Our approach is slightly different, and relies on deformation to an affine hypersurface, together with Artin's vanishing theorem and basic properties of perverse sheaves. |
| title | Weil conjectures and affine hypersurfaces |
| topic | Algebraic Geometry Number Theory 11G25, 14G15 |
| url | https://arxiv.org/abs/2601.20187 |