A criterion for nondensity of integral points
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Date
2024
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Abstract
We give a general criterion for Zariski degeneration of integral points in the complement of a divisor D$D$ with n$n$ components in a variety of dimension n$n$ defined over Q$\mathbb {Q}$ or over a quadratic imaginary field. The key condition is that the intersection of the components of D$D$ is not well approximated by rational points, and we discuss several cases where this assumption is satisfied. We also prove a greatest common divisor (GCD) bound for algebraic points in varieties, which can be of independent interest.