{
  "id": "2405.16514",
  "version": "v1",
  "published": "2024-05-26T10:54:22.000Z",
  "updated": "2024-05-26T10:54:22.000Z",
  "title": "The stable category of monomorphisms between (Gorenstein) projective modules with applications",
  "authors": [
    "Abdolnaser Bahlekeh",
    "Fahimeh Sadat Fotouhi",
    "Mohammad Amin Hamlehdari",
    "Shokrollah Salarian"
  ],
  "comment": "17 pages",
  "categories": [
    "math.RT",
    "math.AC"
  ],
  "abstract": "Let (S; n) be a commutative noetherian local ring and let w in n be non-zero divisor. This paper is concerned with the two categories of monomorphisms between finitely generated (Gorenstein) projective S-modules, such that their cokernels are annihilated by w. It is shown that these categories, which will be denoted by Mon(w;P) and Mon(w; G), are both Frobenius categories with the same projective objects. It is also proved that the stable category Mon(w;P) is triangle equivalent to the category of D-branes of type B, DB(w), which has been introduced by Kontsevich and studied by Orlov. Moreover, it will be observed that the stable categories Mon(w;P) and Mon(w; G) are closely related to the singularity category of the factor ring R = S=(w). Precisely, there is a fully faithful triangle functor from the stable category Mon(w; G) to Dsg(R), which is dense if and only if R (and so S) are Gorenstein rings. Particularly, it is proved that the density of the restriction of this functor to Mon(w;P), guarantees the regularity of the ring S.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-26T10:54:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "projective modules",
      "monomorphisms",
      "stable category mon",
      "applications",
      "gorenstein rings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}