{
  "id": "2109.13330",
  "version": "v2",
  "published": "2021-09-27T20:11:20.000Z",
  "updated": "2021-12-13T18:00:03.000Z",
  "title": "Arithmetic Statistics and noncommutative Iwasawa Theory",
  "authors": [
    "Debanjana Kundu",
    "Antonio Lei",
    "Anwesh Ray"
  ],
  "comment": "50 pages, minor corrections",
  "journal": "Doc. Math. 27, 89-149 (2022)",
  "doi": "10.25537/dm.2022v27",
  "categories": [
    "math.NT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-12-13T18:00:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11G05"
    ],
    "keywords": [
      "noncommutative iwasawa theory",
      "arithmetic statistics",
      "rational elliptic curve",
      "adic lie extension",
      "primary selmer group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}