{
  "id": "2406.14253",
  "version": "v1",
  "published": "2024-06-20T12:25:10.000Z",
  "updated": "2024-06-20T12:25:10.000Z",
  "title": "A new formulation of regular singularity",
  "authors": [
    "Avi Steiner"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We provide an alternative definition for the familiar concept of regular singularity for meromorphic connections. Our new formulation does not use derived categories, and it also avoids the necessity of finding a special good filtration as in the formulation due to Kashiwara--Kawai. Moreover, our formulation provides an explicit algorithm to decide the regular singularity of a meromorphic connection. An important intermediary result, interesting in its own right, is that taking associated graded modules with respect to (not necessarily canonical) $V$-filtrations commutes with non-characteristic restriction. This allows us to reduce the proof of the equivalence of our formulation with the classical concept to the one-dimensional case. In that situation, we extend the well-known one-dimensional Fuchs criterion for ideals in the Weyl algebra to arbitrary holonomic modules over the Weyl algebra equipped with an arbitrary $(-1,1)$-filtration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-20T12:25:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F10",
      "13N10",
      "32S40"
    ],
    "keywords": [
      "regular singularity",
      "formulation",
      "weyl algebra",
      "well-known one-dimensional fuchs criterion",
      "meromorphic connection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}