{
  "id": "math/0311023",
  "version": "v1",
  "published": "2003-11-03T17:42:36.000Z",
  "updated": "2003-11-03T17:42:36.000Z",
  "title": "Some elementary theorems about divisibility of 0-cycles on abelian varieties defined over finite fields",
  "authors": [
    "Hélène Esnault"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "If $X$ is an abelian variety over a field and $L$ is an invertible sheaf, we know that the degree of the 0-cycle $L^g$ is divisible by $g!$. As a 0-cycle, it is not, even over a field of cohomological dimension 1. But we show that over a finite field there is perhaps some hope.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-03T17:42:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian variety",
      "abelian varieties",
      "finite field",
      "elementary theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11023E"
    }
  }
}