{
  "id": "1309.3821",
  "version": "v3",
  "published": "2013-09-16T03:37:21.000Z",
  "updated": "2015-08-28T17:31:24.000Z",
  "title": "Examples of abelian surfaces with everywhere good reduction",
  "authors": [
    "Lassina Dembele",
    "Abhinav Kumar"
  ],
  "comment": "26 pages. Final version (to appear in Mathematische Annalen)",
  "doi": "10.1007/s00208-015-1252-6",
  "categories": [
    "math.NT"
  ],
  "abstract": "We describe several explicit examples of simple abelian surfaces over real quadratic fields with real multiplication and everywhere good reduction. These examples provide evidence for the Eichler-Shimura conjecture for Hilbert modular forms over a real quadratic field. Several of the examples also support a conjecture of Brumer and Kramer on abelian varieties associated to Siegel modular forms with paramodular level structures.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-20T23:06:38.000Z",
      "abstract": "We describe several explicit examples of simple abelian surfaces over real quadratic fields with real multiplication and everywhere good reduction. These examples provide evidence for the Eichler-Shimura conjecture for Hilbert modular forms over a real quadratic field. Several of the examples also support a conjecture of Brumer and Kramer on abelian varieties associated to paramodular forms.",
      "comment": "27 pages. Some typos and minor mistakes have been fixed",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-08-28T17:31:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F41",
      "11F46",
      "11F67",
      "11G10"
    ],
    "keywords": [
      "real quadratic field",
      "simple abelian surfaces",
      "hilbert modular forms",
      "explicit examples",
      "real multiplication"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.3821D"
    }
  }
}