{
  "id": "1110.2918",
  "version": "v2",
  "published": "2011-10-13T12:44:52.000Z",
  "updated": "2012-05-11T15:13:32.000Z",
  "title": "Matrix factorizations over projective schemes",
  "authors": [
    "Jesse Burke",
    "Mark E. Walker"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "We study matrix factorizations of locally free coherent sheaves on a scheme. For a scheme that is projective over an affine scheme, we show that homomorphisms in the homotopy category of matrix factorizations may be computed as the hypercohomology of a certain mapping complex. Using this explicit description, we give another proof of Orlov's theorem that there is a fully faithful embedding of the homotopy category of matrix factorizations into the singularity category of the corresponding zero subscheme. We also give a complete description of the image of this functor.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-11T15:13:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "projective schemes",
      "homotopy category",
      "locally free coherent sheaves",
      "study matrix factorizations",
      "affine scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.2918B"
    }
  }
}