The Brauer–Manin obstruction for curves having split Jacobians
Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 3, pp. 773-777.

Let X𝒜 be a non-constant morphism from a curve X to an abelian variety 𝒜, all defined over a number field k. Suppose that X is a counterexample to the Hasse principle. We give sufficient conditions for the failure of the Hasse principle on X to be accounted for by the Brauer–Manin obstruction. These sufficiency conditions are slightly stronger than assuming that 𝒜(k) and Ш(𝒜/k) are finite.

Soit X𝒜 un morphisme (qui n’est pas constant) d’une courbe X vers une variété abélienne 𝒜, tous définis sur un corps de nombres k. Supposons que X ne satisfait pas le principe de Hasse. Nous donnons des conditions suffisantes pour que l’obstruction de Brauer-Manin soit la seule obstruction au principe de Hasse. Ces conditions suffisantes sont légèrement plus fortes que de supposer que 𝒜(k) et Ш(𝒜/k) sont finis.

DOI: 10.5802/jtnb.469
Samir Siksek 1

1 Department of Mathematics and Statistics Faculty of Science Sultan Qaboos University P.O. Box 36 Al-Khod 123, Oman
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Samir Siksek. The Brauer–Manin obstruction for curves having split Jacobians. Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 3, pp. 773-777. doi : 10.5802/jtnb.469. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.469/

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