On Manin's conjecture for a family of Châtelet surfaces

By R. Bretèche, Tim D Browning, Emmanuel Peyre. 2010

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The Manin conjecture is established for Châtelet surfaces over Q arising as minimal proper smooth models of the surface Y^2+Z^2=f(X) where f is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not satisfy weak approximation.

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fc31600b39d4f269cc6d7f1fe3953ab5f70ba20d