{
  "id": "1711.07552",
  "version": "v1",
  "published": "2017-11-20T21:27:00.000Z",
  "updated": "2017-11-20T21:27:00.000Z",
  "title": "On Jacobians with group action and coverings",
  "authors": [
    "Sebastián Reyes-Carocca",
    "Rubí E. Rodríguez"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $S$ be a compact Riemann surface and let $H$ be a finite group. It is known that if $H$ acts on $S$ then there is a $H$-equivariant isogeny decomposition of the Jacobian variety $JS$ of $S,$ called the group algebra decomposition of $JS$ with respect to $H.$ If $S_1 \\to S_2$ is a regular covering map, then it is also known that the group algebra decomposition of $JS_1$ induces an isogeny decomposition of $JS_2.$ In this article we deal with the converse situation. More precisely, we prove that the group algebra decomposition can be lifted under regular covering maps, under appropriate conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-20T21:27:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H40",
      "14H37",
      "14L30"
    ],
    "keywords": [
      "group algebra decomposition",
      "group action",
      "regular covering map",
      "compact riemann surface",
      "equivariant isogeny decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}