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The period-index problem in WC-groups I: elliptic curves

Pete L. Clark
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Abstract

Let E/K be an elliptic curve defined over a number field, and let p be a prime number such that E(K) has full p-torsion. We show that the order of the p-part of the Shafarevich-Tate group of E/L is unbounded as L varies over degree p extensions of K. The proof uses O'Neil's period-index obstruction. We deduce the result from the fact that, under the same hypotheses, there exist infinitely many elements of the Weil-Chatelet group of E/K of period p and index p^2.

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Pete L. Clark. 2004-06-07. The period-index problem in WC-groups I: elliptic curves. https://arxiv.org/abs/math/0406131

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