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arXiv · 2106.11337

Divisibility of polynomials and degeneracy of integral points

Erwan Rousseau·Julie Tzu-Yueh Wang·Amos Turchet
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Abstract

We prove several statements about arithmetic hyperbolicity of certain blow-up varieties. As a corollary we obtain multiple examples of simply connected quasi-projective varieties that are pseudo-arithmetically hyperbolic. This generalizes results of Corvaja and Zannier obtained in dimension 2 to arbitrary dimension. The key input is an application of the Ru-Vojta's strategy. We also obtain the analogue results for function fields and Nevanlinna theory with the goal to apply them in a future paper in the context of Campana's conjectures.

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Erwan Rousseau, Julie Tzu-Yueh Wang, Amos Turchet. 2021-06-21. Divisibility of polynomials and degeneracy of integral points. https://arxiv.org/abs/2106.11337

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