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We prove these conjectures for the total space of fibrations, over curves with finite Tate-Shafarevich group, into rationally connected varieties which satisfy weak approximation, under an abelianness assumption on the singular fibers.\n\n----\n\nSoit X une vari\\'et\\'e propre et lisse sur un corps de nombres k. 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Conjectures on the image of the Chow group of zero-cycles of X in the product of the corresponding groups over all completions of k were put forward by Colliot-Th\\'el\\`ene, Kato and Saito. We prove these conjectures for the total space of fibrations, over curves with finite Tate-Shafarevich group, into rationally connected varieties which satisfy weak approximation, under an abelianness assumption on the singular fibers.\n\n----\n\nSoit X une vari\\'et\\'e propre et lisse sur un corps de nombres k. 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