Approximating rational points on surfaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929264644849664 |
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| author | Lehmann, Brian McKinnon, David Satriano, Matthew |
| author_facet | Lehmann, Brian McKinnon, David Satriano, Matthew |
| contents | Let $X$ be a smooth projective algebraic variety over a number field $k$ and $P$ in $X(k)$. In 2007, the second author conjectured that, in a precise sense, if rational points on $X$ are dense enough, then the best rational approximations to $P$ must lie on a curve. We present a strategy for deducing a slightly weaker conjecture from Vojta's conjecture, and execute this strategy for the full conjecture for split surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02480 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximating rational points on surfaces Lehmann, Brian McKinnon, David Satriano, Matthew Algebraic Geometry Number Theory 14G05 (Primary) 14E30 (Secondary) Let $X$ be a smooth projective algebraic variety over a number field $k$ and $P$ in $X(k)$. In 2007, the second author conjectured that, in a precise sense, if rational points on $X$ are dense enough, then the best rational approximations to $P$ must lie on a curve. We present a strategy for deducing a slightly weaker conjecture from Vojta's conjecture, and execute this strategy for the full conjecture for split surfaces. |
| title | Approximating rational points on surfaces |
| topic | Algebraic Geometry Number Theory 14G05 (Primary) 14E30 (Secondary) |
| url | https://arxiv.org/abs/2403.02480 |