{
  "id": "2309.06754",
  "version": "v1",
  "published": "2023-09-13T07:04:08.000Z",
  "updated": "2023-09-13T07:04:08.000Z",
  "title": "Explicit Riemann-Roch spaces in the Hilbert class field",
  "authors": [
    "Jean-Marc Couveignes",
    "Jean Gasnier"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\mathbf K$ be a finite field, $X$ and $Y$ two curves over $\\mathbf K$, and $Y\\rightarrow X$ an unramified abelian cover with Galois group $G$. Let $D$ be a divisor on $X$ and $E$ its pullback on $Y$. Under mild conditions the linear space associated with $E$ is a free ${\\mathbf K}[G]$-module. We study the algorithmic aspects and applications of these modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-13T07:04:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert class field",
      "explicit riemann-roch spaces",
      "algorithmic aspects",
      "galois group",
      "mild conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}