{
  "id": "2103.02092",
  "version": "v1",
  "published": "2021-03-02T23:45:37.000Z",
  "updated": "2021-03-02T23:45:37.000Z",
  "title": "Anticyclotomic $\\largeμ$-invariants of residually reducible Galois Representations",
  "authors": [
    "Debanjana Kundu",
    "Anwesh Ray"
  ],
  "comment": "16 pages, comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $E$ be an elliptic curve over an imaginary quadratic field $K$, and $p$ be an odd prime such that the residual representation $E[p]$ is reducible. The $\\mu$-invariant of the fine Selmer group of $E$ over the anticyclotomic $\\mathbb{Z}_p$-extension of $K$ is studied. We do not impose the Heegner hypothesis on $E$, thus allowing certain primes of bad reduction to decompose infinitely in the anticyclotomic $\\mathbb{Z}_p$-extension. It is shown that the fine $\\mu$-invariant vanishes if certain explicit conditions are satisfied. Further, a partial converse is proven.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-02T23:45:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11R23"
    ],
    "keywords": [
      "residually reducible galois representations",
      "anticyclotomic",
      "imaginary quadratic field",
      "fine selmer group",
      "elliptic curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}