{
  "id": "math/0611815",
  "version": "v2",
  "published": "2006-11-27T11:08:38.000Z",
  "updated": "2007-06-05T16:50:02.000Z",
  "title": "Cohomology of moduli spaces of curves of genus three via point counts",
  "authors": [
    "Jonas Bergström"
  ],
  "comment": "25 pages, shortened version",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this article we consider the moduli space of smooth $n$-pointed non-hyperelliptic curves of genus 3. In the pursuit of cohomological information about this space, we make $\\mathbb{S}_n$-equivariant counts of its numbers of points defined over finite fields for $n \\leq 7$. Combining this with results on the moduli spaces of smooth pointed curves of genus 0, 1 and 2, and the moduli space of smooth hyperelliptic curves of genus 3, we can determine the $\\mathbb{S}_n$-equivariant Galois and Hodge structure of the ($\\ell$-adic respectively Betti) cohomology of the moduli space of stable curves of genus 3 for $n \\leq 5$ (to obtain $n \\leq 7$ we would need counts of ``8-pointed curves of genus 2'').",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-06-05T16:50:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "11G20"
    ],
    "keywords": [
      "moduli space",
      "point counts",
      "cohomology",
      "smooth hyperelliptic curves",
      "adic respectively betti"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11815B"
    }
  }
}