{
  "id": "2301.09073",
  "version": "v1",
  "published": "2023-01-22T08:05:48.000Z",
  "updated": "2023-01-22T08:05:48.000Z",
  "title": "The $μ$-invariant change for abelian varieties over finite $p$-extensions of global fields",
  "authors": [
    "Ki-Seng Tan",
    "Fabien Trihan",
    "Kwok-Wing Tsoi"
  ],
  "comment": "31 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We extend the work of Lai, Longhi, Suzuki, the first two authors and study the change of $\\mu$-invariants, with respect to a finite Galois p-extension $K'/K$, of an ordinary abelian variety $A$ over a $\\mathbb{Z}_p^d$-extension of global fields $L/K$ (whose characteristic is not necessarily positive) that ramifies at a finite number of places at which $A$ has ordinary reductions. We obtain a lower bound for the $\\mu$-invariant of $A$ along $LK'/K'$ and deduce that the $\\mu$-invariant of an abelian variety over a global field can be chosen as big as needed. Finally, in the case of elliptic curve over a global function field that has semi-stable reduction everywhere we are able to improve the lower bound in terms of invariants that arise from the supersingular places of $A$ and certain places that split completely over $L/K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-22T08:05:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11G10",
      "11S40",
      "14J27"
    ],
    "keywords": [
      "global field",
      "invariant change",
      "lower bound",
      "global function field",
      "ordinary abelian variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}