25 citations · 111 across the 35 of their papers we have counts for
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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…
On the distribution of rational points on ramified covers of abelian varieties
Pietro Corvaja, Julian Lawrence Demeio, Ariyan Javanpeykar +2
We prove new results on the distribution of rational points on ramified covers of abelian varieties over finitely generated fields of characteristic zero. For example, given a…
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…
Good reduction and cyclic covers
Ariyan Javanpeykar, Daniel Loughran, Siddharth Mathur
We prove finiteness results for sets of varieties over number fields with good reduction outside a given finite set of places using cyclic covers. We obtain a version of the Shafar…
The Shafarevich conjecture revisited: Finiteness of pointed families of polarized varieties
Ariyan Javanpeykar, Ruiran Sun, Kang Zuo
Motivated by Lang-Vojta's conjectures on hyperbolic varieties, we prove a new version of the Shafarevich conjecture in which we establish the finiteness of pointed families of pola…
Rational points and ramified covers of products of two elliptic curves
Ariyan Javanpeykar
Corvaja and Zannier conjectured that an abelian variety over a number field satisfies a modified version of the Hilbert property. We investigate their conjecture for products of el…
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…