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math.NT2010★ 8 cited
Potential Sha for abelian varieties
Brendan Creutz
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),…
math.NT2010★ 5 cited
A Grunwald-Wang type theorem for abelian varieties
Brendan Creutz
Let A be an abelian variety over a number field k. We show that weak approximation holds in the Weil-Châtelet group of A/k but that it may fail when one restricts to the n-torsion…