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Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions

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.
Type
Journal Article
Type of thesis
Series
Citation
Delbourgo, 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
Date
2017
Publisher
Springer
Degree
Supervisors
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.