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

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Conceição R.

Acta Arithmetica

2013

tom 161

nr 4

351-370

We construct isotrivial and non-isotrivial elliptic curves over $𝔽_q(t)$ 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 $𝔽_q(t)$ 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.

Ograniczanie wyników

1 Acta Arithmetica

1 Conceição R.

1 2013

Wyniki wyszukiwania

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