Density of rational points on isotrivial rational elliptic surfaces
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 weakweak approximation. Our results are conditional on the finiteness of TateShafarevich groups for elliptic curves over the field of rational numbers.
 Publication:

arXiv eprints
 Pub Date:
 November 2009
 arXiv:
 arXiv:0911.3881
 Bibcode:
 2009arXiv0911.3881V
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 14 G05;
 11 G05
 EPrint:
 Latex