Rational points and ramified covers of products of two elliptic curves

2020/03/19 by Javanpeykar, Ariyan
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2003.08625

Abstract

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 elliptic curves using Kawamata's structure result for ramified covers of abelian varieties, and Faltings's finiteness theorem for rational points on higher genus curves.

Related

• Ramified covers of abelian varieties over torsion fields
• Rational curves and the Hilbert Property on Jacobian Kummer varieties
• The rational points on certain Abelian varieties over function fields
• On the distribution of rational points on ramified covers of abelian varieties
• Products of varieties with many integral points