On a problem posed by Bjorn Poonen
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917614201077760 |
|---|---|
| author | Rawson, James |
| author_facet | Rawson, James |
| contents | Bjorn Poonen asked whether there exists a polynomial giving a surjection $\mathbb{Z} \times \mathbb{Z} \to \mathbb{N}$. We answer this question in the negative, conditional on a conjecture of Vojta. More precisely, we show that if such a function exists, there is a family of open surfaces with dense integral points despite the surfaces being of log general type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a problem posed by Bjorn Poonen Rawson, James Number Theory Bjorn Poonen asked whether there exists a polynomial giving a surjection $\mathbb{Z} \times \mathbb{Z} \to \mathbb{N}$. We answer this question in the negative, conditional on a conjecture of Vojta. More precisely, we show that if such a function exists, there is a family of open surfaces with dense integral points despite the surfaces being of log general type. |
| title | On a problem posed by Bjorn Poonen |
| topic | Number Theory |
| url | https://arxiv.org/abs/2403.09440 |