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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
Software:
ecdata
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References:
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