{
  "id": "1207.4810",
  "version": "v1",
  "published": "2012-07-19T20:53:57.000Z",
  "updated": "2012-07-19T20:53:57.000Z",
  "title": "Genus one curves and Brauer-Severi varieties",
  "authors": [
    "Aise Johan de Jong",
    "Wei Ho"
  ],
  "comment": "comments welcome",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let K be a field. Let A be a central simple algebra over K and let X be the associated Brauer-Severi variety over K. It has recently been asked if there exists a genus 1 curve C over K such that K(C) splits A. In other words, is there a genus one curve C over K with a morphism to X? In this short note, we explicitly construct such a curve in the case where X has dimension at most 4 (equivalently, when A has degree at most 5).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-19T20:53:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central simple algebra",
      "associated brauer-severi variety",
      "short note",
      "explicitly construct"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.4810D"
    }
  }
}