{
  "id": "1902.08331",
  "version": "v1",
  "published": "2019-02-22T01:47:29.000Z",
  "updated": "2019-02-22T01:47:29.000Z",
  "title": "Ample line bundles, global generation and $K_0$ on quasi-projective derived schemes",
  "authors": [
    "Toni Annala"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "The purpose of this note is to extend some classical results on quasi-projective schemes to the setting of derived algebraic geometry. Namely, we want to show that any vector bundle on a derived scheme admitting an ample line bundle can be twisted to be globally generated. Moreover, we provide a presentation of $K^0(X)$ as the Grothendieck group of vector bundles modulo exact sequences on any quasi-projective derived scheme $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-22T01:47:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ample line bundle",
      "quasi-projective derived scheme",
      "global generation",
      "vector bundles modulo exact sequences",
      "derived algebraic geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}