Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions
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
Permanent Research Commons link: https://hdl.handle.net/10289/12260
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.
This is an author’s accepted version of an article published in the journal: The Ramanujan Journal. © Springer Science+Business Media New York 2016.