Boundedness in families with applications to arithmetic hyperbolicity

Boundedness in families with applications to arithmetic hyperbolicity

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 irre...

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Veröffentlicht in:arXiv.org 2023-11
Hauptverfasser: Raymond van Bommel, Ariyan Javanpeykar, Kamenova, Ljudmila
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Arithmetic
Mathematics - Algebraic Geometry
Mathematics - Number Theory
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description 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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subjects Algebra
Arithmetic
Mathematics - Algebraic Geometry
Mathematics - Number Theory
title Boundedness in families with applications to arithmetic hyperbolicity
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