{
  "id": "2312.17597",
  "version": "v1",
  "published": "2023-12-29T13:22:49.000Z",
  "updated": "2023-12-29T13:22:49.000Z",
  "title": "The correspondence between silting objects and $t$-structures for non-positive dg algebras",
  "authors": [
    "Riku Fushimi"
  ],
  "comment": "15 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We establish a bijective correspondence between isomorphism classes of basic silting objects of $\\mathsf{per}(A)$ and algebraic $t$-structures of $\\mathsf{D}_{\\rm fd}(A)$ for locally finite non-positive dg algebra $A$ over a field $k$ (more generally, we work in the setting of ST-pair inside an algebraic triangulated category). For a non-positive (topologically) homologically smooth dg $k$-algebra $A$ whose zeroth cohomology is finite-dimensional, or for a non-positive proper dg $k$-algebra $A$, the one-to-one correspondence between isomorphism classes of basic silting objects of $\\mathsf{per}(A)$ and algebraic $t$-structures on $\\mathsf{D}_{\\rm fd}(A)$ was already known. The main result of this paper generalizes the above two results to locally finite non-positive dg $k$-algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-29T13:22:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E35",
      "16E45",
      "18G80"
    ],
    "keywords": [
      "structures",
      "correspondence",
      "basic silting objects",
      "isomorphism classes",
      "locally finite non-positive dg algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}