{
  "id": "1801.07383",
  "version": "v1",
  "published": "2018-01-23T03:12:36.000Z",
  "updated": "2018-01-23T03:12:36.000Z",
  "title": "A class number formula for Picard modular surfaces",
  "authors": [
    "Aaron Pollack",
    "Shrenik Shah"
  ],
  "categories": [
    "math.NT",
    "math.AG",
    "math.RT"
  ],
  "abstract": "We investigate arithmetic aspects of the middle degree cohomology of compactified Picard modular surfaces $X$ attached to the unitary similitude group $\\mathrm{GU}(2,1)$ for an imaginary quadratic extension $E/\\mathbf{Q}$. We construct new Beilinson--Flach classes on $X$ and compute their Archimedean regulator. We obtain a special value formula involving a non-critical $L$-value of the degree six standard $L$-function, a Whittaker period, and the regulator. This provides evidence for Beilinson's conjecture in this setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-23T03:12:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67",
      "11G18",
      "11G40",
      "14G35",
      "19E15"
    ],
    "keywords": [
      "class number formula",
      "middle degree cohomology",
      "special value formula",
      "compactified picard modular surfaces",
      "unitary similitude group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}