{
  "id": "2302.13480",
  "version": "v1",
  "published": "2023-02-27T02:33:07.000Z",
  "updated": "2023-02-27T02:33:07.000Z",
  "title": "The length of the tail of affine equations of Drinfeld modules and their duals",
  "authors": [
    "A. Grishkov",
    "D. Logachev"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The authors defined in \"$h^1\\ne h_1$ for Anderson t-motives\" ([GL21]) the notion of an affine equation associated to a t-motive $M$, and conjectured that the length of its tail is $n$ -- the dimension of $M$. This conjecture was checked in [GL21] for some t-motives of ranks $r=4$ and 5, and of $n=2$. We show in the present paper that it is true for Drinfeld modules and their duals. Since the dimension of the dual of a Drinfeld module of rank $r$ is $r-1$, this is the first checking of this conjecture for $n>2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-27T02:33:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G09"
    ],
    "keywords": [
      "drinfeld module",
      "affine equation",
      "conjecture",
      "anderson t-motives"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}