Principe local-global pour les zéro-cycles sur certaines fibrations au-dessus d'une courbe : I

Details Principe local-global pour les zéro-cycles sur certaines fibrations au-dessus d'une courbe : I Principe local-global pour les zéro-cycles sur certaines fibrations au-dessus d'une courbe : I

2010-06-13

arxiv.org/abs/1006.2572v4

Mathematics

Algebraic Geometry

Some mistakes are corrected, unnecessary arguments are omitted. 20 pages

Scientific paper

Let $X$ be a smooth projective variety over a number field, fibered over a curve, with geometrically integral fibers. We prove that, supposing the finiteness of $\sha(Jac(C))$, if the fibers over a generalised Hilbertian subset satisfy the Hasse principle (resp. weak approximation), then the Brauer-Manin obstruction coming from the base curve is the only obstruction to the Hasse principle (resp. to weak approximation) for zero-cycles of degree 1 on $X$.

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