Products of varieties with many integral points
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918219698143232 |
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| author | Luger, Cedric |
| author_facet | Luger, Cedric |
| contents | Corvaja and Zannier asked whether a smooth projective integral variety with a dense set of rational points over a number field satisfies the weak Hilbert property. We introduce an extension of the weak Hilbert property for schemes over arithmetic base rings by considering near-integral points, extending Corvaja-Zannier's question beyond the projective case. Building on work of Bary-Soroker-Fehm-Petersen and Corvaja-Demeio-Javanpeykar-Lombardo-Zannier, we prove several properties of this more general notion, in particular its persistence under products. We also answer positively Corvaja-Zannier's question for all algebraic groups over finitely generated fields of characteristic zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05203 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Products of varieties with many integral points Luger, Cedric Algebraic Geometry Primary: 14G99. Secondary: 14G05, 14G40 Corvaja and Zannier asked whether a smooth projective integral variety with a dense set of rational points over a number field satisfies the weak Hilbert property. We introduce an extension of the weak Hilbert property for schemes over arithmetic base rings by considering near-integral points, extending Corvaja-Zannier's question beyond the projective case. Building on work of Bary-Soroker-Fehm-Petersen and Corvaja-Demeio-Javanpeykar-Lombardo-Zannier, we prove several properties of this more general notion, in particular its persistence under products. We also answer positively Corvaja-Zannier's question for all algebraic groups over finitely generated fields of characteristic zero. |
| title | Products of varieties with many integral points |
| topic | Algebraic Geometry Primary: 14G99. Secondary: 14G05, 14G40 |
| url | https://arxiv.org/abs/2401.05203 |