The period-index problem in WC-groups I: elliptic curves |
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Authors: | Pete L Clark |
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Institution: | Department of Mathematics and Statistics, McGill University, 1126 Burnside Hall, 805 Sherbrooke West, Montreal, QC, Canada H3A 2K6 |
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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-Châtelet group of E/K of period p and index p2. |
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Keywords: | Elliptic curves Galois cohomology Shafarevich-Tate group Period-index problem |
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