2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108995We wish to give a short elementary proof of S. Saito's result that the Brauer-Manin obstruction for zero-cycles of degree 1 is the only one for curves, supposing the finiteness of the Tate-Shafarevich-group $\sha^1(A)$ of the Jacobian variety. In fact we show that we only need a conjecturally finite part of the Brauer-group for this obstruction to be the only one. We also comment on the situation in higher dimensions12 pagesNumber TheoryAlgebraic Geometry11G30; 16K50; 14L10text