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

• Autorzy: Ricardo P. Conceição
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11G35: Varieties over global fields
• 11G05: Elliptic curves over global fields
• 14H05: Algebraic functions; function fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 4
• Strony: 351-370

Daty

wydano

2013

Twórcy

autor

Ricardo P. Conceição

• Oxford College of Emory University, 100 Hamill Street, Oxford, GA 30054, U.S.A.

Identyfikatory

DOI

10.4064/aa161-4-3