{
  "id": "math/0106055",
  "version": "v2",
  "published": "2001-06-08T13:43:57.000Z",
  "updated": "2003-11-06T10:35:50.000Z",
  "title": "Abelian varieties with group action",
  "authors": [
    "H. Lange",
    "S. Recillas"
  ],
  "comment": "30 pages, corrected version abbriviated to 21 pages, to appear in Journ. Reine Angew. Mathem",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let G be a finite group acting on a smooth projective curve X. This induces an action of G on the Jacobian JX of X and thus a decomposition of JX up to isogeny. The most prominent example of such a situation is the group G of two elements. Let X --> Y denote the corresponding quotient map. Then JX is isogenous to the product of JY with the Prym variety of X/Y. In this paper some general results on group actions on abelian varieties are given and applied to deduce a decomposition of the jacobian JX for arbitrary group actions. Several examples are given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-11-06T10:35:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14K05",
      "14H40"
    ],
    "keywords": [
      "abelian varieties",
      "jacobian jx",
      "arbitrary group actions",
      "finite group",
      "smooth projective curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......6055L"
    }
  }
}