Kundu, Debanjana; Lei, Antonio; Ray, Anwesh

Arithmetic statistics and noncommutative Iwasawa theory

Doc. Math. 27, 89-149 (2022)
DOI: 10.25537/dm.2022v27.89-149
Communicated by Otmar Venjakob


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.

Mathematics Subject Classification

11R23, 11G05


arithmetic statistics, noncommutative Iwasawa theory, Selmer groups, Euler characteristics, Akashi series, growth of Mordell-Weil ranks


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Kundu, Debanjana
Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2
Lei, Antonio
Département de Mathématiques et de Statistique, Université Laval, Pavillion Alexandre-Vachon, 1045 Avenue de la Médecine, Québec, QC, Canada G1V 0A6
Ray, Anwesh
Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2