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The Brauer-Manin obstruction for curves having split Jacobians. (English) Zbl 1076.14033
Summary: Let $$X\to{\mathcal A}$$ be a non-constant morphism from a curve $$X$$ to an abelian variety $${\mathcal A}$$, 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 $${\mathcal A}(k)$$ and Ш$$({\mathcal A}/k)$$ are finite.

##### MSC:
 14H25 Arithmetic ground fields for curves
ecdata
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##### References:
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