{
  "id": "1212.4308",
  "version": "v1",
  "published": "2012-12-18T11:14:56.000Z",
  "updated": "2012-12-18T11:14:56.000Z",
  "title": "Modularity of Calabi--Yau varieties: 2011 and beyond",
  "authors": [
    "Noriko Yui"
  ],
  "comment": "33 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "This paper presents the current status on modularity of Calabi-Yau varieties since the last update in 2003. We will focus on Calabi-Yau varieties of dimension at most three. Here modularity refers to at least two different types: arithmetic modularity and geometric modularity. These will include: (1) the modularity (automorphy) of Galois representations of Calabi-Yau varieties (or motives) defined over Q or number fields, (2) the modularity of solutions of Picard--Fuchs differential equations of families of Calabi-Yau varieties, and mirror maps (mirror moonshine), (3) the modularity of generating functions of invariants counting certain quantities on Calabi-Yau varieties, and (4) the modularity of moduli for families of Calabi-Yau varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-18T11:14:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G42",
      "11F80",
      "11G40",
      "14J15",
      "14J32",
      "14J33"
    ],
    "keywords": [
      "calabi-yau varieties",
      "picard-fuchs differential equations",
      "geometric modularity",
      "galois representations",
      "current status"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.4308Y"
    }
  }
}