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Elliptic Curves Over Function Fields with a Large Set of Integral Points by Conceição, Ricardo is a scholarly article available to read on EtoBox.

What is Elliptic Curves Over Function Fields with a Large Set of Integral Points about?

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.

Author

Conceição, Ricardo

Published

2009

Language

EN