Generalized Campana points and adelic approximation on toric varieties
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912022365470720 |
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| author | Moerman, Boaz |
| author_facet | Moerman, Boaz |
| contents | We introduce a general framework for studying special subsets of rational points on an algebraic variety, termed $\mathcal{M}$-points. The notion of $\mathcal{M}$-points generalizes the concepts of integral points, Campana points and Darmon points. We introduce and study $M$-approximation over number fields and function fields, which is a notion that generalizes weak and strong approximation. We show that this property implies that the set of $\mathcal{M}$-points is not thin. We then give a simple characterisation of when a split toric variety satisfies $M$-approximation, generalizing work of Nakahara and Streeter. Further, we determine when the set of $\mathcal{M}$-points on a split toric variety is thin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Campana points and adelic approximation on toric varieties Moerman, Boaz Algebraic Geometry Number Theory 14G12 (Primary), 14M25, 14G05, 11G35 (Secondary) We introduce a general framework for studying special subsets of rational points on an algebraic variety, termed $\mathcal{M}$-points. The notion of $\mathcal{M}$-points generalizes the concepts of integral points, Campana points and Darmon points. We introduce and study $M$-approximation over number fields and function fields, which is a notion that generalizes weak and strong approximation. We show that this property implies that the set of $\mathcal{M}$-points is not thin. We then give a simple characterisation of when a split toric variety satisfies $M$-approximation, generalizing work of Nakahara and Streeter. Further, we determine when the set of $\mathcal{M}$-points on a split toric variety is thin. |
| title | Generalized Campana points and adelic approximation on toric varieties |
| topic | Algebraic Geometry Number Theory 14G12 (Primary), 14M25, 14G05, 11G35 (Secondary) |
| url | https://arxiv.org/abs/2407.03048 |