{
  "id": "1808.05119",
  "version": "v1",
  "published": "2018-08-15T15:09:29.000Z",
  "updated": "2018-08-15T15:09:29.000Z",
  "title": "A DG-enhancement of D(QCoh(X)) with applications in deformation theory",
  "authors": [
    "Francesco Meazzini"
  ],
  "categories": [
    "math.AG",
    "math.CT"
  ],
  "abstract": "It is well-known that DG-enhancements of D(QCoh(X)) are all equivalent to each other, see [23]. Here we present an explicit model which leads to applications in deformation theory. In particular, we shall describe three models for derived endomorphisms of a quasi-coherent sheaf F on a finite-dimensional Noetherian separated scheme (even if F does not admit a locally free resolution). Moreover, these complexes are endowed with DG-Lie algebra structures, which we prove to control infinitesimal deformations of F.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-15T15:09:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05",
      "14D15",
      "16W50",
      "18G55"
    ],
    "keywords": [
      "deformation theory",
      "dg-enhancement",
      "applications",
      "control infinitesimal deformations",
      "dg-lie algebra structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}