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math.AG2019
Finiteness properties of pseudo-hyperbolic varieties
Ariyan Javanpeykar, Junyi Xie
Motivated by Lang-Vojta's conjecture, we show that the set of dominant rational self-maps of an algebraic variety over a number field with only finitely many rational points in any…
math.AG2019
Integral points on algebraic subvarieties of period domains: from number fields to finitely generated fields
Ariyan Javanpeykar, Daniel Litt
We show that for a variety which admits a quasi-finite period map, finiteness (resp.~non-Zariski-density) of -integral points implies finiteness (resp.~non-Zariski-density) of p…
math.AG2019
Boundedness in families with applications to arithmetic hyperbolicity
Raymond van Bommel, Ariyan Javanpeykar, Ljudmila Kamenova
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…