{
  "id": "2205.06615",
  "version": "v1",
  "published": "2022-05-13T13:06:52.000Z",
  "updated": "2022-05-13T13:06:52.000Z",
  "title": "Fine Selmer groups of modular forms",
  "authors": [
    "Sören Kleine",
    "Katharina Müller"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We compare the Iwasawa invariants of fine Selmer groups of $p$-adic Galois representations over admissible $p$-adic Lie extensions of a number field $K$ to the Iwasawa invariants of ideal class groups along these Lie extensions. More precisely, let $K$ be a number field, let $V$ be a $p$-adic representation of the absolute Galois group $G_K$ of $K$, and choose a $G_K$-invariant lattice ${T \\subseteq V}$. We study the fine Selmer groups of ${A = V/T}$ over suitable $p$-adic Lie extensions $K_\\infty/K$, comparing their corank and $\\mu$-invariant to the corank and the $\\mu$-invariant of the Iwasawa module of ideal class groups in $K_\\infty/K$. In the second part of the article, we compare the Iwasawa $\\mu$- and $l_0$-invariants of the fine Selmer groups of CM modular forms on the one hand and the Iwasawa invariants of ideal class groups on the other hand over trivialising multiple $\\mathbb{Z}_p$-extensions of $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-13T13:06:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23"
    ],
    "keywords": [
      "fine selmer groups",
      "ideal class groups",
      "adic lie extensions",
      "iwasawa invariants",
      "number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}