{
  "id": "1602.06811",
  "version": "v1",
  "published": "2016-02-22T15:16:38.000Z",
  "updated": "2016-02-22T15:16:38.000Z",
  "title": "Unique factorization of principally polarized abelian varieties",
  "authors": [
    "Bruce W. Jordan",
    "Allan G. Keeton",
    "Bjorn Poonen"
  ],
  "comment": "5 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Shimura proved that each principally polarized abelian variety over $\\mathbf{C}$ admits a unique factorization into irreducible principally polarized abelian varieties. We give an exposition of his result, and generalize to an arbitrary ground field $k$. If $k$ is separably closed, the irreducible factors are in bijection with the irreducible components of a theta divisor over $k$ giving rise to the polarization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-22T15:16:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "principally polarized abelian variety",
      "unique factorization",
      "arbitrary ground field",
      "irreducible principally polarized abelian varieties",
      "theta divisor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160206811J"
    }
  }
}