{
  "id": "2009.02533",
  "version": "v1",
  "published": "2020-09-05T13:34:15.000Z",
  "updated": "2020-09-05T13:34:15.000Z",
  "title": "Explicit description of isogeny and isomorphism classes of Drinfeld modules over finite field",
  "authors": [
    "Sedric Nkotto Nkung Assong"
  ],
  "comment": "This paper is extracted from my PhD thesis that I defended recently at the institute of Mathematics of the university of Kassel in Germany",
  "categories": [
    "math.NT"
  ],
  "abstract": "When travelling from the number fields theory to the function fields theory, one cannot miss the deep analogy between rank 1 Drinfeld modules and the group of root of unity and the analogy between rank 2 Drinfeld modules and elliptic curves. But so far, there is no known structure in number fields theory that is analogous to the Drinfeld modules of higher rank r > 2. In this paper we investigate the classes of those Drinfeld modules of higher rank r > 2. We describe explicitly the Weil polynomials defining the isogeny classes of rank r Drinfeld modules for any rank r > 2. our explicit description of the Weil polynomials depends heavily on Yu's classification of isogeny classes (analogue of Honda-Tate at abelian varieties). Actually Yu has also explicitly did that work for r = 2. To complete the classification, we define the new notion of fine isomorphy invariants for any rank r Drinfeld module and we prove that the fine isomorphy invariants together with J-invariants completely determine the L-isomorphism classes of rank r Drinfeld modules defined over the finite field L.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-05T13:34:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "drinfeld module",
      "explicit description",
      "finite field",
      "isomorphism classes",
      "fine isomorphy invariants"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "de",
      "license": "arXiv",
      "status": "editable"
    }
  }
}