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Dec 29, 2009 at 16:40 history edited Idoneal CC BY-SA 2.5
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Dec 29, 2009 at 16:39 comment added Idoneal Yes, that's right.
Dec 29, 2009 at 16:25 comment added David E Speyer The pair (Selmer's curve, Jacobian of Selmer's curve) are everywhere locally isomorphic, but not globally so. However, Selmer's curve is not an abelian variety, because it has no rational points. So this is very close to, but not the same as, what was asked for.
Dec 29, 2009 at 16:20 history answered Idoneal CC BY-SA 2.5