{
  "id": "1510.02839",
  "version": "v1",
  "published": "2015-10-09T22:16:53.000Z",
  "updated": "2015-10-09T22:16:53.000Z",
  "title": "Period and index for higher genus curves",
  "authors": [
    "Shahed Sharif"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Given a curve $C$ over a field $K$, the period of $C/K$ is the gcd of degrees of $K$-rational divisor classes, while the index is the gcd of degrees of $K$-rational divisors. S. Lichtenbaum showed that the period and index must satisfy certain divisibility conditions. For given admissible period, index, and genus, we show that there exists a curve $C$ and a number field $K$ with these desired invariants, as long as the index is not divisible by $4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-09T22:16:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher genus curves",
      "rational divisor classes",
      "number field",
      "divisibility conditions",
      "lichtenbaum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151002839S"
    }
  }
}