Boundedness in families with applications to arithmetic hyperbolicity

Raymond van Bommel; Ariyan Javanpeykar; Ljudmila Kamenova

doi:10.1112/jlms.12847

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arXiv · 1907.11225

Boundedness in families with applications to arithmetic hyperbolicity

Raymond van Bommel·Ariyan Javanpeykar·Ljudmila Kamenova

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Abstract

Motivated by conjectures of Demailly, Green-Griffiths, Lang, and Vojta, we show that several notions related to hyperbolicity behave similarly in families. We apply our results to show the persistence of arithmetic hyperbolicity along field extensions for projective normal surfaces with nonzero irregularity. These results rely on the mild boundedness of semi-abelian varieties. We also introduce and study the notion of pseudo-algebraic hyperbolicity which extends Demailly's notion of algebraic hyperbolicity for projective schemes.

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Raymond van Bommel, Ariyan Javanpeykar, Ljudmila Kamenova. 2023-11-18. Boundedness in families with applications to arithmetic hyperbolicity. https://doi.org/10.1112/jlms.12847

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