Principe local-global pour les zéro-cycles sur les surfaces réglées

Let be a number field, a smooth projective curve, and a smooth projective surface which is a conic bundle over . Let be the relative Chow group, which is the kernel of the projection map on Chow groups of zero-cycles. For each place of , one may consider the relative Chow group . Under minor assumptions, we identify the diagonal image of in the product of all as the kernel of the natural pairing with the Brauer group of . When is an elliptic curve with finite Tate-Shafarevich group, under minor assumptions, we show that the Brauer-Manin obstruction to the existence of a zero-cycle of degree one on is the only obstruction.