Elliptic curves over function fields with a large set of integral points

Volume 161 / 2013

Ricardo P. Conceição 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.

Authors

  • Ricardo P. ConceiçãoOxford College of Emory University
    100 Hamill Street
    Oxford, GA 30054, U.S.A.
    e-mail

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