English

On Manin's conjecture for a family of Ch\^atelet surfaces

Number Theory 2010-02-02 v1

Abstract

The Manin conjecture is established for Ch\^atelet 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.

Keywords

Cite

@article{arxiv.1002.0255,
  title  = {On Manin's conjecture for a family of Ch\^atelet surfaces},
  author = {R. de la Bretèche and T. D. Browning and E. Peyre},
  journal= {arXiv preprint arXiv:1002.0255},
  year   = {2010}
}