Arithmetic statistics and noncommutative Iwasawa theory

Let p be an odd prime. Associated to a pair (E, \mathcal{F}_\infty) consisting of a rational elliptic curve E and a p -adic Lie extension \mathcal{F}_\infty of \mathbb{Q} , is the p -primary Selmer group \mathrm{Sel}_{p^{\infty}}(E/\mathcal{F}_\infty) of E over \mathcal{F}_\infty . In this paper, we study the arithmetic statistics for the algebraic structure of this Selmer group. The results provide insights into the asymptotics for the growth of Mordell-Weil ranks of elliptic curves in noncommutative towers.