{
  "id": "1302.4537",
  "version": "v4",
  "published": "2013-02-19T08:08:42.000Z",
  "updated": "2014-10-09T20:46:10.000Z",
  "title": "E_1-degeneration of the irregular Hodge filtration (with an appendix by Morihiko Saito)",
  "authors": [
    "Hélène Esnault",
    "Claude Sabbah",
    "Jeng-Daw Yu"
  ],
  "comment": "v2:54 pages. Some corrections. v3: 49 pages. Some improvements and simplifications. v4: revised version, few typos corrected",
  "categories": [
    "math.AG"
  ],
  "abstract": "For a regular function f on a smooth complex quasi-projective variety, J.-D. Yu introduced in arXiv:1203.2338 a filtration (the irregular Hodge filtration) on the de Rham complex with twisted differential d+df, extending a definition of Deligne in the case of curves. In this article, we show the degeneration at E_1 of the spectral sequence attached to the irregular Hodge filtration, by using the method of arXiv:0804.4328. We also make explicit the relation with a complex introduced by M. Kontsevich and give details on its proof of the corresponding E_1 degeneration, by reduction to characteristic p, when the pole divisor of the function is reduced with normal crossings. In Appendix E, M. Saito gives a different proof of the latter statement with a possibly non reduced normal crossing pole divisor.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-01-30T10:55:19.000Z",
      "comment": "v2:54 pages. Some corrections. v3: 49 pages. Some improvements and simplifications",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-10-09T20:46:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F40",
      "32S35",
      "32S40"
    ],
    "keywords": [
      "irregular hodge filtration",
      "morihiko saito",
      "normal crossing pole divisor",
      "reduced normal crossing pole",
      "non reduced normal crossing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.4537E"
    }
  }
}