{
  "id": "2401.15631",
  "version": "v1",
  "published": "2024-01-28T11:31:21.000Z",
  "updated": "2024-01-28T11:31:21.000Z",
  "title": "Maps between schematic semi-graded rings",
  "authors": [
    "Andrés Chacón",
    "María Camila Ramírez",
    "Armando Reyes"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AG",
    "math.QA"
  ],
  "abstract": "Motivated by Smith's work \\cite{Smith2003, Smith2016} on maps between non-commu\\-tative projective spaces of the form ${\\rm Proj}_{nc} A$ in the setting of non-commutative projective geometry developed by Rosenberg and Van den Bergh, and the notion of schematicness introduced by Van Oystaeyen and Willaert \\cite{VanOystaeyenWillaert1995} to $\\mathbb{N}$-graded rings with the aim of formulating a non-commutative scheme theory \\`a la Grothendieck \\cite{EGAII1961}, in this paper we consider a first approach to maps in the Smith's sense in the more general setting of non-commutative projective spaces over semi-graded rings defined by Lezama and Latorre \\cite{LezamaLatorre2017}. We extend Smith's key result \\cite[Theorem 3.2]{Smith2003}, \\cite[Theorem 1.2]{Smith2016} from the category of schematic $\\mathbb{N}$-graded rings to the category of schematic semi-graded rings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-28T11:31:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A22",
      "16S38",
      "16S80",
      "16U20",
      "16W60"
    ],
    "keywords": [
      "schematic semi-graded rings",
      "projective spaces",
      "van den bergh",
      "smiths sense",
      "first approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}