Groupe de Brauer et points entiers de deux familles de surfaces cubiques affines

Jean-Louis Colliot-Thélène, Olivier Wittenberg

Let a be a nonzero integer. If a is not congruent to 4 or 5 modulo 9 then there is no Brauer-Manin obstruction to the existence of integers x, y, z such that x^3+y^3+z^3=a. In addi…