3 papers
math.AG2025
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…
math.NT2025
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 c…
math.NT2025
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…