{
  "id": "2304.02778",
  "version": "v1",
  "published": "2023-04-05T22:50:45.000Z",
  "updated": "2023-04-05T22:50:45.000Z",
  "title": "Automorphism groups of curves over arbitrary fields",
  "authors": [
    "Daniel Bragg"
  ],
  "comment": "19 pages. comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that if $K$ is an arbitrary field and $G$ is a finite group then there exists a curve over $K$ with automorphism group $G$. We also reduce the inverse Galois problem for function fields over an arbitrary field $K$ to the case of $K(T)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-05T22:50:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H37",
      "12F12",
      "12F10"
    ],
    "keywords": [
      "arbitrary field",
      "automorphism group",
      "inverse galois problem",
      "finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}