Potential Sha for abelian varieties

Details Potential Sha for abelian varieties Potential Sha for abelian varieties

2010-10-16

arxiv.org/abs/1010.3349v2

Journal of Number Theory 131,pp. 2162-2174 (2011)

Mathematics

Number Theory

Version 2: improved exposition and corrected various small errors

Scientific paper

10.1016/j.jnt.2011.05.013

We show that the p-torsion in the Tate-Shafarevich group of any principally
polarized abelian variety over a number field is unbounded as one ranges over
extensions of degree O(p), the implied constant depending only on the dimension
of the abelian variety.

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