9 papers · 1 filter
Algebraic intermediate hyperbolicities
Antoine Etesse, Ariyan Javanpeykar, Erwan Rousseau
We extend Lang's conjectures to the setting of intermediate hyperbolicity and prove two new results motivated by these conjectures. More precisely, we first extend the notion of al…
Albanese maps and fundamental groups of varieties with many rational points over function fields
Ariyan Javanpeykar, Erwan Rousseau
We investigate properties of the Albanese map and the fundamental group of a complex projective variety with many rational points over some function field, and prove that every lin…
The Lang-Vojta conjectures on projective pseudo-hyperbolic varieties
Ariyan Javanpeykar
These notes grew out of a mini-course given from May 13th to May 17th at UQAM in Montreal during a workshop on Diophantine Approximation and Value Distribution Theory. We start wit…
Urata's theorem in the logarithmic case and applications to integral points
Ariyan Javanpeykar, Aaron Levin
Urata showed that a pointed compact hyperbolic variety admits only finitely many maps from a pointed curve. We extend Urata's theorem to the setting of (not necessarily compact) hy…
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…
Arithmetic hyperbolicity: automorphisms and persistence
Ariyan Javanpeykar
We show that if the automorphism group of a projective variety is torsion, then it is finite. Motivated by Lang's conjecture on rational points of hyperbolic varieties, we use this…