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The period-index problem in WC-groups II: abelian varieties

Pete L. Clark
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Abstract

We study the relationship between the period and the index of a principal homogeneous space over an abelian variety, obtaining results which generalize work of Cassels and Lichtenbaum on curves of genus one. In addition, we show that the p-torsion in the Shafarevich-Tate group of a fixed abelian variety over a number field k grows arbitrarily large when considered over field extensions l/k of bounded degree. Essential use is made of an abelian variety version of O'Neil's period-index obstruction.

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Pete L. Clark. 2004-06-08. The period-index problem in WC-groups II: abelian varieties. https://arxiv.org/abs/math/0406135

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