A higher dimensional Hilbert irreducibility theorem
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866915322379894784 |
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| author | Bresciani, Giulio |
| author_facet | Bresciani, Giulio |
| contents | Assuming the weak Bombieri-Lang conjecture, we prove that a generalization of Hilbert's irreducibility theorem holds for families of geometrically mordellic varieties (for instance, families of hyperbolic curves). As an application we prove that, assuming Bombieri-Lang, there are no polynomial bijections $\mathbb{Q} \times \mathbb{Q} \to \mathbb{Q}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_01090 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A higher dimensional Hilbert irreducibility theorem Bresciani, Giulio Number Theory Algebraic Geometry Assuming the weak Bombieri-Lang conjecture, we prove that a generalization of Hilbert's irreducibility theorem holds for families of geometrically mordellic varieties (for instance, families of hyperbolic curves). As an application we prove that, assuming Bombieri-Lang, there are no polynomial bijections $\mathbb{Q} \times \mathbb{Q} \to \mathbb{Q}$. |
| title | A higher dimensional Hilbert irreducibility theorem |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2101.01090 |