Density of rational points on isotrivial rational elliptic surfaces
Number Theory
2012-06-13 v3 Algebraic Geometry
Abstract
For a large class of isotrivial rational elliptic surfaces (with section), we show that the set of rational points is dense for the Zariski topology, by carefully studying variations of root numbers among the fibers of these surfaces. We also prove that these surfaces satisfy a variant of weak-weak approximation. Our results are conditional on the finiteness of Tate-Shafarevich groups for elliptic curves over the field of rational numbers.
Keywords
Cite
@article{arxiv.0911.3881,
title = {Density of rational points on isotrivial rational elliptic surfaces},
author = {Anthony Várilly-Alvarado},
journal= {arXiv preprint arXiv:0911.3881},
year = {2012}
}
Comments
Latex; 26 pages. To appear in Algebra and Number Theory