{
  "id": "math/0312474",
  "version": "v5",
  "published": "2003-12-29T07:00:20.000Z",
  "updated": "2006-03-28T01:38:23.000Z",
  "title": "Cherednik algebras and Hilbert schemes in characteristic p",
  "authors": [
    "Roman Bezrukavnikov",
    "Michael Finkelberg",
    "Victor Ginzburg"
  ],
  "comment": "Appendices by Pavel Etingof and Vadim Vologodsky",
  "categories": [
    "math.RT",
    "math.AG",
    "math.QA"
  ],
  "abstract": "We prove a localization theorem for the type A rational Cherednik algebra H_c=H_{1,c} over an algebraic closure of the finite field F_p. In the most interesting special case where the parameter c takes values in F_p, we construct an Azumaya algebra A_c on Hilb^n, the Hilbert scheme of n points in the plane, such that the algebra of global sections of A_c is isomorphic to H_c. Our localisation theorem provides an equivalence between the bounded derived categories of H_c-modules and sheaves of coherent A_c-modules on the Hilbert scheme, respectively. Furthermore, we show that the Azumaya algebra splits on the formal completion of each fiber of the Hilbert-Chow morphism. This provides a link between our results and those of Bridgeland-King-Reid and Haiman.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2006-03-28T01:38:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert scheme",
      "characteristic",
      "rational cherednik algebra",
      "azumaya algebra splits",
      "algebraic closure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12474B"
    }
  }
}