$CH_{0}$-trivialit\'e universelle d'hypersurfaces cubiques presque   diagonales
  Toute hypersurface cubique lisse complexe de dimension au moins 2 dont l'\'equation est donn\'ee par l'annulation d'une somme de formes cubiques \`a variables s\'epar\'ees, chaque forme impliquant au plus trois variables, est universellement $CH_{0}$-triviale.   ---   If a smooth cubic hypersurface of dimension at least 2 is defined by the vanishing of a sum of cubic forms in independent variables and each of these forms involves at most 3 variables, then the cubic hypersurface is universally $CH_{0}$-trivial : there is an integral Chow decomposition of the diagonal. 
Jean-Louis Colliot-Th\'el\`ene
math.AG