Density of Châtelet surfaces failing the Hasse principle

Abstract

Châtelet surfaces provide a rich source of geometrically rational surfaces which do not always satisfy the Hasse principle. Restricting attention to a special class of Châtelet surfaces, we investigate the frequency that such counter-examples arise over the rationals.

arXiv comment52 pages; minor changes

Cited by in corpus (4)

• Failures of the Integral Hasse Principle for Affine Quadric Surfaces
• Schinzel Hypothesis on average and rational points
• Rational points on del Pezzo surfaces of degree four
• Local-global principles for semi-integral points on Markoff orbifold pairs