{
  "id": "1903.07010",
  "version": "v1",
  "published": "2019-03-17T01:05:01.000Z",
  "updated": "2019-03-17T01:05:01.000Z",
  "title": "On line bundles in derived algebraic geometry",
  "authors": [
    "Toni Annala"
  ],
  "comment": "9 pages, comments welcome",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "We give examples of derived schemes $X$ and a line bundle $\\Ls$ on the truncation $tX$ so that $\\Ls$ does not extend to the original derived scheme $X$. In other words the pullback map $\\Pic(X) \\to \\Pic(tX)$ is not surjective. Our examples have the further property that, while their truncations are projective hypersurfaces, they fail to have any nontrivial line bundles, and hence they are not quasi-projective.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-17T01:05:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derived algebraic geometry",
      "nontrivial line bundles",
      "truncation",
      "original derived scheme",
      "pullback map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}