{
  "id": "math/0702838",
  "version": "v3",
  "published": "2007-02-27T15:19:13.000Z",
  "updated": "2008-09-15T11:08:40.000Z",
  "title": "Deformation theory of objects in homotopy and derived categories I: general theory",
  "authors": [
    "Alexander I. Efimov",
    "Valery A. Lunts",
    "Dmitri O. Orlov"
  ],
  "comment": "Alexander Efimov is a new co-author of this paper. Besides some minor changes, Proposition 7.1 and Theorem 8.1 were corrected",
  "journal": "Adv. Math. 222 (2009), no. 2, 359--401",
  "categories": [
    "math.AG",
    "math.CT"
  ],
  "abstract": "This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module $E$ over a DG category we define four deformation functors $\\Def ^{\\h}(E)$, $\\coDef ^{\\h}(E)$, $\\Def (E)$, $\\coDef (E)$. The first two functors describe the deformations (and co-deformations) of $E$ in the homotopy category, and the last two - in the derived category. We study their properties and relations. These functors are defined on the category of artinian (not necessarily commutative) DG algebras.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-09-15T11:08:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derived category",
      "general theory",
      "dg category",
      "general deformation theory",
      "first paper"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2838E"
    }
  }
}