{
  "id": "2204.13381",
  "version": "v1",
  "published": "2022-04-28T09:53:54.000Z",
  "updated": "2022-04-28T09:53:54.000Z",
  "title": "The Hodge filtrations of monodromic mixed Hodge modules and the irregular Hodge filtrations",
  "authors": [
    "Takahiro Saito"
  ],
  "comment": "56 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "For an algebraic vector bundle $E$ over a smooth algebraic variety $X$, a monodromic $D$-module on $E$ is decomposed into a direct sum of some $O$-modules on $X$. We show that the Hodge filtration of a monodromic mixed Hodge module is decomposed with respect to the decomposition of the underlying $D$-module. By using this result, we endow the Fourier-Laplace transform $M^{\\wedge}$ of the underlying $D$-module $M$ of a monodromic mixed Hodge module with a mixed Hodge module structure. Moreover, we describe the irregular Hodge filtration on $M^{\\wedge}$ concretely and show that it coincides with the Hodge filtration at all integer indices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-28T09:53:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monodromic mixed hodge module",
      "irregular hodge filtration",
      "algebraic vector bundle",
      "smooth algebraic variety",
      "mixed hodge module structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}