4 papers
Counting rational points on elliptic and hyperelliptic curves over function fields
Jean Gillibert, Emmanuel Hallouin, Aaron Levin
Combining -descent techniques with Riemann-Roch and Bézout's theorems, we give an upper bound on the number of rational points of bounded height on elliptic and hyperelliptic cu…
Symmetric products and puncturing Campana-special varieties
Finn Bartsch, Ariyan Javanpeykar, Aaron Levin
We give a counterexample to the Arithmetic Puncturing Conjecture and Geometric Puncturing Conjecture of Hassett-Tschinkel using symmetric powers of uniruled surfaces, and propose a…
A New Diophantine Approximation Inequality on Surfaces and Its Applications
Keping Huang, Aaron Levin, Zheng Xiao
We prove a Diophantine approximation inequality for closed subschemes on surfaces which can be viewed as a joint generalization of recent inequalities of Ru-Vojta and Heier-Levin i…
Arithmetic rank bounds for abelian varieties over function fields
Félix Baril Boudreau, Jean Gillibert, Aaron Levin
It follows from the Grothendieck-Ogg-Shafarevich formula that the rank of an abelian variety (with trivial trace) defined over the function field of a curve is bounded by a quantit…