Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions
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Accepted version, 568.0Kb
Citation
Export citationDelbourgo, D., & Lei, A. (2017). Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions. Ramanujan Journal, 43(1), 29–68. https://doi.org/10.1007/s11139-016-9785-1
Permanent Research Commons link: https://hdl.handle.net/10289/12260
Abstract
Let E/Q be an elliptic curve, p > 3 a good ordinary prime for E, and K∞ a p-adic Lie extension of a number field k. Under some standard hypotheses, we study the asymptotic growth in both the Mordell–Weil rank and Shafarevich–Tate group for E over a tower of extensions K ₙ/ₖ inside K∞; we obtain lower bounds on the former, and upper bounds on the latter’s size.
Date
2017Type
Publisher
Springer
Rights
This is an author’s accepted version of an article published in the journal: The Ramanujan Journal. © Springer Science+Business Media New York 2016.