{
  "id": "1310.2508",
  "version": "v5",
  "published": "2013-10-09T14:54:21.000Z",
  "updated": "2014-11-14T22:28:07.000Z",
  "title": "Cohomology of local systems on the moduli of principally polarized abelian surfaces",
  "authors": [
    "Dan Petersen"
  ],
  "comment": "18 pages. v3: Added a proof of a dimension formula for vector-valued Siegel cusp forms for Sp(4,Z) of weight three, previously conjectured by Ibukiyama. v4: Many minor changes and improvements. Final version, to appear in Pacific Journal of Mathematics",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let A_2 be the moduli stack of principally polarized abelian surfaces and V a smooth l-adic sheaf on A_2 associated to an irreducible rational finite dimensional representation of Sp(4). We give an explicit expression for the cohomology of V in any degree in terms of Tate type classes and Galois representations attached to elliptic and Siegel cusp forms. This confirms a conjecture of Faber and van der Geer. As an application we prove a dimension formula for vector-valued Siegel cusp forms for Sp(4,Z) of weight three, which had been conjectured by Ibukiyama.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-05-22T11:02:02.000Z",
      "comment": "18 pages. v3: Added a proof of a dimension formula for vector-valued Siegel cusp forms for Sp(4,Z) of weight three, previously conjectured by Ibukiyama",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2014-11-14T22:28:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F46",
      "14K10",
      "11G18",
      "11F67",
      "11F75"
    ],
    "keywords": [
      "principally polarized abelian surfaces",
      "local systems",
      "siegel cusp forms",
      "cohomology",
      "irreducible rational finite dimensional representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.2508P"
    }
  }
}