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2011 Density of rational points on isotrivial rational elliptic surfaces
Anthony Várilly-Alvarado
Algebra Number Theory 5(5): 659-690 (2011). DOI: 10.2140/ant.2011.5.659


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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Anthony Várilly-Alvarado. "Density of rational points on isotrivial rational elliptic surfaces." Algebra Number Theory 5 (5) 659 - 690, 2011.


Received: 22 September 2010; Revised: 26 September 2010; Accepted: 24 October 2010; Published: 2011
First available in Project Euclid: 20 December 2017

zbMATH: 1276.11114
MathSciNet: MR2889751
Digital Object Identifier: 10.2140/ant.2011.5.659

Primary: 11G35
Secondary: 11G05 , 14G05

Keywords: del Pezzo surfaces , rational elliptic surfaces , root numbers

Rights: Copyright © 2011 Mathematical Sciences Publishers

Vol.5 • No. 5 • 2011
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