{
  "id": "math/0412367",
  "version": "v3",
  "published": "2004-12-18T19:02:34.000Z",
  "updated": "2005-03-31T20:20:40.000Z",
  "title": "Endomorphism Rings and Isogenies Classes for Drinfeld Modules of Rank 2 Over Finite Fields",
  "authors": [
    "Mohamed Ahmed Mohamed Saadbouh"
  ],
  "comment": "19",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $\\Phi $ be a Drinfeld $\\mathbf{F}_{q}[T]$-module of rank 2, over a finite field $L$, a finite extension of $n$ degrees of a finite field with $q$ elements $\\mathbf{F}_{q}$. Let $m$ be the extension degrees of $ L$ over the field $\\mathbf{F}_{q}[T]/P$, $P$ is the $\\mathbf{F}%_{q}[T]$-characteristic of $L$, and $d$ the degree of the polynomial $P$. We will discuss about a many analogies points with elliptic curves. We start by the endomorphism ring of a Drinfeld $\\mathbf{F}_{q}[T]$-module of rank 2, End$_{L}\\Phi $, and we specify the maximality conditions and non maximality conditions as a $\\mathbf{F}_{q}[T]$-order in the ring of division End$_{L}\\Phi \\otimes _{\\mathbf{F}_{q}[T]}% \\mathbf{F}_{q}(T)$, in the next point we will interested to the characteristic polynomial of a Drinfeld module of rank 2 and used it to calculate the number of isogeny classes for such module, at last we will interested to the Characteristic of Euler-Poincare $\\chi_{\\Phi}$ and we will calculated the cardinal of this ideals.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-03-31T20:20:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J32",
      "81T30"
    ],
    "keywords": [
      "finite field",
      "drinfeld module",
      "isogenies classes",
      "endomorphism ring",
      "non maximality conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12367S"
    }
  }
}