{
  "id": "1701.03744",
  "version": "v1",
  "published": "2017-01-13T17:32:19.000Z",
  "updated": "2017-01-13T17:32:19.000Z",
  "title": "Grothendieck groups of categories of abelian varieties",
  "authors": [
    "Ari Shnidman"
  ],
  "comment": "Comments welcome!",
  "categories": [
    "math.AG",
    "math.KT",
    "math.NT"
  ],
  "abstract": "We compute the Grothendieck group of the category of abelian varieties over an algebraically closed field $k$. We also compute the Grothendieck group of the category of $A$-isotypic abelian varieties, for any simple abelian variety $A$, assuming $k$ has characteristic 0, and for any elliptic curve $A$ in any characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-13T17:32:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "14K99",
      "19A99"
    ],
    "keywords": [
      "grothendieck group",
      "simple abelian variety",
      "isotypic abelian varieties",
      "characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}