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

Ricardo P. Conceição. "Elliptic curves over function fields with a large set of integral points." Acta Arithmetica 161.4 (2013): 351-370. <http://eudml.org/doc/279829>.

@article{RicardoP2013,
abstract = {We construct isotrivial and non-isotrivial elliptic curves over $_q(t)$ 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 $_q(t)$ 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 = {Ricardo P. Conceição},
journal = {Acta Arithmetica},
keywords = {elliptic curve; integral point; Lang-Vojta conjecture; function field},
language = {eng},
number = {4},
pages = {351-370},
title = {Elliptic curves over function fields with a large set of integral points},
url = {http://eudml.org/doc/279829},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Ricardo P. Conceição
TI - Elliptic curves over function fields with a large set of integral points
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 4
SP - 351
EP - 370
AB - We construct isotrivial and non-isotrivial elliptic curves over $_q(t)$ 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 $_q(t)$ 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.
LA - eng
KW - elliptic curve; integral point; Lang-Vojta conjecture; function field
UR - http://eudml.org/doc/279829
ER -