March 4, 2024Open Access

Approximating rational points on surfaces

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Resumen

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.

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Cite This Study

Lehmann et al. (Mon,) studied this question.

synapsesocial.com/papers/68e75ddfb6db6435876d52fa https://doi.org/https://doi.org/10.48550/arxiv.2403.02480

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