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arXiv · 2311.17701

A criterion for non-density of integral points

Natalia Garcia-Fritz·Hector Pasten
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Abstract

We give a general criterion for Zariski degeneration of integral points in the complement of a divisor $D$ with $n$ components in a variety of dimension $n$ defined over $\mathbb{Q}$ or over a quadratic imaginary field. The key condition is that the intersection of the components of $D$ is not well-approximated by rational points, and we discuss several cases where this assumption is satisfied. We also prove a GCD bound for algebraic points in varieties, which can be of independent interest.

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Natalia Garcia-Fritz, Hector Pasten. 2023-11-29. A criterion for non-density of integral points. https://arxiv.org/abs/2311.17701

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