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If $C$ is a genus-2 curve over a number field $k$, the problem of determining the (finite) set $C(k)$ is best understood by looking at the finitely generated group of rational points on its Jacobian. We attempt to find nontrivial elements in the Tate-Shafarevich group of this Jacobian by means of a Brauer-Manin obstruction on an associated K3 surface.
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