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Jan 22, 2016 at 14:55 history edited Maxim CC BY-SA 3.0
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Jan 22, 2016 at 14:14 comment added Matthias Wendt Section 3 of Lang-Tate "Principal homogeneous spaces over abelian varieties" discusses that the specialization map for abelian varieties induces isomorphisms on $n$-torsion points if $n$ is not divisible by the residue characteristic and the abelian variety has good reduction. The link between the Jacobian of reduction and the reduction of the Jacobian should be discussed in Bosch-Lütkebohmert-Raynaud "Néron models".
Jan 22, 2016 at 12:37 history asked Maxim CC BY-SA 3.0