Rational points on del Pezzo surfaces of low degree
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929205913059328 |
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| author | Glas, Jakob Hochfilzer, Leonhard |
| author_facet | Glas, Jakob Hochfilzer, Leonhard |
| contents | We give upper bounds for the number of rational points of bounded anti-canonical height on del Pezzo surfaces of degree at most five over any global field whose characteristic is not equal to two or three. For number fields these results are conditional on a conjecture relating the rank of an elliptic curve to its conductor, while they are unconditional in positive characteristic. For quartic or quintic del Pezzo surfaces with a conic bundle structure, we establish even stronger estimates unconditionally as long as the characteristic is not two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04759 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational points on del Pezzo surfaces of low degree Glas, Jakob Hochfilzer, Leonhard Number Theory Algebraic Geometry 11D45, 11G05, 11G35, 14G05, 11H06 We give upper bounds for the number of rational points of bounded anti-canonical height on del Pezzo surfaces of degree at most five over any global field whose characteristic is not equal to two or three. For number fields these results are conditional on a conjecture relating the rank of an elliptic curve to its conductor, while they are unconditional in positive characteristic. For quartic or quintic del Pezzo surfaces with a conic bundle structure, we establish even stronger estimates unconditionally as long as the characteristic is not two. |
| title | Rational points on del Pezzo surfaces of low degree |
| topic | Number Theory Algebraic Geometry 11D45, 11G05, 11G35, 14G05, 11H06 |
| url | https://arxiv.org/abs/2401.04759 |