{
  "id": "2405.14330",
  "version": "v1",
  "published": "2024-05-23T09:00:16.000Z",
  "updated": "2024-05-23T09:00:16.000Z",
  "title": "Derived category of equivariant coherent sheaves on a smooth toric variety and Koszul duality",
  "authors": [
    "Valery A. Lunts"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a smooth toric variety defined by the fan {\\Sigma} . We consider {\\Sigma} as a finite set with topology and define a natural sheaf of graded algebras A_{\\Sigma} on {\\Sigma} . The category of modules over A_{\\Sigma} is studied (together with other related categories). This leads to a certain combinatorial Koszul duality equivalence. We describe the equivariant category of coherent sheaves coh_{X,T} and a related (slightly bigger) equivariant category O_{X,T}-mod in terms of sheaves of modules over the sheaf of algebras A_{\\Sigma} . Eventually (for a complete X ) the combinatorial Koszul duality is interpreted in terms of the Serre functor on D^b(coh_{X,T})",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-23T09:00:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smooth toric variety",
      "equivariant coherent sheaves",
      "derived category",
      "combinatorial koszul duality equivalence",
      "equivariant category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}