Density of rational points on isotrivial rational elliptic surfaces

Details Density of rational points on isotrivial rational elliptic surfaces Density of rational points on isotrivial rational elliptic surfaces

2009-11-19

arxiv.org/abs/0911.3881v3

Mathematics

Number Theory

Latex; 26 pages. To appear in Algebra and Number Theory

Scientific paper

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.

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