{
  "id": "2406.13418",
  "version": "v1",
  "published": "2024-06-19T10:15:02.000Z",
  "updated": "2024-06-19T10:15:02.000Z",
  "title": "Filtrations of torsion classes in proper abelian subcategories",
  "authors": [
    "Anders S. Kortegaard"
  ],
  "comment": "12 pages, comments are welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "In an abelian category $\\mathscr{A}$, we can generate torsion pairs from tilting objects of projective dimension $\\leq 1$. However, when we look at tilting objects of projective dimension $2$, there is no longer a natural choice of an associated torsion pair. Instead of trying to generate a torsion pair, Jensen, Madsen and Su generated a triple of extension closed classes that can filter any objects of $\\mathscr{A}$. We generalize this result to proper abelian subcategories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-19T10:15:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E10",
      "18G80"
    ],
    "keywords": [
      "proper abelian subcategories",
      "torsion classes",
      "filtrations",
      "generate torsion pairs",
      "tilting objects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}