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arXiv · 2109.13330

Arithmetic Statistics and noncommutative Iwasawa Theory

Debanjana Kundu·Antonio Lei·Anwesh Ray
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Abstract

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 $Sel_{p^\infty}(E/\mathcal{F}_\infty)$ 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.

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Debanjana Kundu, Antonio Lei, Anwesh Ray. 2021-12-13. Arithmetic Statistics and noncommutative Iwasawa Theory. https://doi.org/10.25537/dm.2022v27

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