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We prove that the Brauer-Manin obstruction is the only obstruction to theHasse principle and to the weak approximation for zero-cycles on certainfibrations over a smooth curve or over the projective space. The principalnovelty is that the arithmetic hypotheses are supposed only on the fibres overa generalized Hilbertian subset.

Astuce de Salberger et z\'ero-cycles sur certaines fibrations