{
  "id": "math/9801119",
  "version": "v3",
  "published": "1998-01-26T20:00:04.000Z",
  "updated": "2000-04-07T17:15:23.000Z",
  "title": "Categorical Mirror Symmetry: The Elliptic Curve",
  "authors": [
    "Alexander Polishchuk",
    "Eric Zaslow"
  ],
  "comment": "harvmac, 29 pages (big); updated with corrections",
  "journal": "Adv.Theor.Math.Phys.2:443-470,1998",
  "categories": [
    "math.AG",
    "hep-th"
  ],
  "abstract": "We describe an isomorphism of categories conjectured by Kontsevich. If $M$ and $\\widetilde{M}$ are mirror pairs then the conjectural equivalence is between the derived category of coherent sheaves on $M$ and a suitable version of Fukaya's category of Lagrangian submanifolds on $\\widetilde{M}.$ We prove this equivalence when $M$ is an elliptic curve and $\\widetilde{M}$ is its dual curve, exhibiting the dictionary in detail.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2000-04-07T17:15:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "categorical mirror symmetry",
      "elliptic curve",
      "lagrangian submanifolds",
      "mirror pairs",
      "fukayas category"
    ],
    "tags": [
      "journal article",
      "famous paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 485000,
      "adsabs": "1998math......1119P"
    }
  }
}