{
  "id": "2008.07136",
  "version": "v1",
  "published": "2020-08-17T07:59:24.000Z",
  "updated": "2020-08-17T07:59:24.000Z",
  "title": "Taylor coefficients of Anderson generating functions and Drinfeld torsion extensions",
  "authors": [
    "Andreas Maurischat",
    "Rudolph Perkins"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT",
    "math.RA"
  ],
  "abstract": "We generalize our work on Carlitz prime power torsion extension to torsion extensions of Drinfeld modules of arbitrary rank. As in the Carlitz case, we give a description of these extensions in terms of evaluations of Anderson generating functions and their hyperderivatives at roots of unity. We also give a direct proof that the image of the Galois representation attached to the $\\mathfrak{p}$-adic Tate module lies in the $\\mathfrak{p}$-adic points of the motivic Galois group. This is a generalization of the corresponding result of Chang and Papanikolas for the $t$-adic case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-17T07:59:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J93"
    ],
    "keywords": [
      "anderson generating functions",
      "drinfeld torsion extensions",
      "taylor coefficients",
      "carlitz prime power torsion extension",
      "adic tate module lies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}