Elliptic curves over function fields with a large set of integral points
Volume 161 / 2013
Acta Arithmetica 161 (2013), 351-370
MSC: 11G05, 11G35, 14H05.
DOI: 10.4064/aa161-4-3
Abstract
We construct isotrivial and non-isotrivial elliptic curves over $\mathbb {F}_q(t)$ with an arbitrarily large set of separable integral points. As an application of this construction, we prove that there are isotrivial log-general type varieties over $\mathbb {F}_q(t)$ with a Zariski dense set of separable integral points. This provides a counterexample to a natural translation of the Lang–Vojta conjecture to the function field setting. We also show that our main result provides examples of elliptic curves with an explicit and arbitrarily large set of linearly independent points.
