Density of Ch\^atelet surfaces failing the Hasse principle
  Ch\^atelet surfaces provide a rich source of geometrically rational surfaces which do not always satisfy the Hasse principle. Restricting attention to a special class of Ch\^atelet surfaces, we investigate the frequency that such counter-examples arise over the rationals. 
R. de la Bret\`eche, T. D. Browning
math.NT math.AG