{
  "id": "math/0006213",
  "version": "v1",
  "published": "2000-06-28T07:25:14.000Z",
  "updated": "2000-06-28T07:25:14.000Z",
  "title": "Nonabelian mixed Hodge structures",
  "authors": [
    "Ludmil Katzarkov",
    "Tony Pantev",
    "Carlos Simpson"
  ],
  "comment": "126 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We propose a definition of ``nonabelian mixed Hodge structure'' together with a construction associating to a smooth projective variety $X$ and to a nonabelian mixed Hodge structure $V$, the ``nonabelian cohomology of $X$ with coefficients in $V$'' which is a (pre-)nonabelian mixed Hodge structure denoted $H=Hom(X_M, V)$. We describe the basic definitions and then give some conjectures saying what is supposed to happen. At the end we compute an example: the case where $V$ has underlying homotopy type the complexified 2-sphere, and mixed Hodge structure coming from its identification with $\\pp ^1$. For this example we show that $Hom (X_M,V)$ is a namhs for any smooth projective variety $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-06-28T07:25:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smooth projective variety",
      "nonabelian mixed hodge structure",
      "nonabelian cohomology",
      "underlying homotopy type",
      "basic definitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 126,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......6213K"
    }
  }
}