{
  "id": "math/0701502",
  "version": "v1",
  "published": "2007-01-18T14:22:30.000Z",
  "updated": "2007-01-18T14:22:30.000Z",
  "title": "Monodromy eigenvalues and zeta functions with differential forms",
  "authors": [
    "Willem Veys"
  ],
  "comment": "To appear in Advances in Mathematics. 17 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "For a complex polynomial or analytic function f, one has been studying intensively its so-called local zeta functions or complex powers; these are integrals of |f|^{2s}w considered as functions in s, where the w are differential forms with compact support. There is a strong correspondence between their poles and the eigenvalues of the local monodromy of f. In particular Barlet showed that each monodromy eigenvalue of f is of the form exp(a2i\\pi), where a is such a pole. We prove an analogous result for similar p-adic complex powers, called Igusa (local) zeta functions, but mainly for the related algebro-geometric topological and motivic zeta functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-18T14:22:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "32S40",
      "11S80"
    ],
    "keywords": [
      "monodromy eigenvalue",
      "differential forms",
      "similar p-adic complex powers",
      "motivic zeta functions",
      "local zeta functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1502V"
    }
  }
}