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 weak-weak approximation. Our results are conditional on the finiteness of Tate-Shafarevich groups for elliptic curves over the field of rational numbers.

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

References in corpus (2)

• On the Birch-Swinnerton-Dyer quotients modulo squares
• Rational points on certain elliptic surfaces

Cited by in corpus (8)

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• Density of rational points on a family of del Pezzo surfaces of degree one
• Tamagawa number divisibility of central $L$-values of twists of the Fermat elliptic curve
• A classical family of elliptic curves having rank one and the $2$-primary part of their Tate-Shafarevich group non-trivial
• On central $L$-values and the growth of the $3$-part of the Tate-Shafarevich group