{
  "id": "math/0403478",
  "version": "v5",
  "published": "2004-03-27T13:49:42.000Z",
  "updated": "2006-03-25T03:36:03.000Z",
  "title": "Finite groups of symplectic automorphisms of K3 surfaces in positive characteristic",
  "authors": [
    "Igor Dolgachev",
    "JongHae Keum"
  ],
  "comment": "The final version to appear in Annals of Mathematics. 42 pages",
  "categories": [
    "math.AG",
    "math.GR"
  ],
  "abstract": "We show that Mukai's classification of finite groups which may act symplectically on a complex K3 surface extends to positive characteristic $p$ under the assumptions that (i) the order of the group is coprime to $p$ and (ii) either the surface or its quotient is not birationally isomorphic to a supersingular K3 surface with Artin invariant 1. In the case without the assumption (ii) we classify all possible new groups which may appear. We prove that the assumption on the order of the group is always satisfied if $p > 11$ and if $p=2,3,5,11$ we give examples of K3 surfaces with finite symplectic automorphism groups of order divisible by $p$ which are not contained in Mukai's list.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2006-03-25T03:36:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28",
      "20B25"
    ],
    "keywords": [
      "finite groups",
      "positive characteristic",
      "finite symplectic automorphism groups",
      "complex k3 surface extends",
      "supersingular k3 surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3478D"
    }
  }
}