Geodesic
Arithmetic statistics and noncommutative Iwasawa theory
Documenta mathematica, Tome 27 (2022), pp. 89-149.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 11R23, 11G05
Keywords: arithmetic statistics, noncommutative Iwasawa theory, Selmer groups, Euler characteristics, Akashi series, growth of Mordell-Weil ranks 
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     title = {Arithmetic statistics and noncommutative {Iwasawa} theory},
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Kundu, Debanjana; Lei, Antonio; Ray, Anwesh. Arithmetic statistics and noncommutative Iwasawa theory. Documenta mathematica, Tome 27 (2022), pp. 89-149. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a64/