{
  "id": "2308.06633",
  "version": "v1",
  "published": "2023-08-12T18:57:26.000Z",
  "updated": "2023-08-12T18:57:26.000Z",
  "title": "On the cohomology of GL_2 and SL_2 over imaginary quadratic fields",
  "authors": [
    "Herbert Gangl",
    "Paul E. Gunnells",
    "Jonathan Hanke",
    "Dan Yasaki"
  ],
  "categories": [
    "math.NT",
    "math.RA"
  ],
  "abstract": "We report on computations of the cohomology of GL_2(O_D) and SL_2(O_D), where D<0 is a fundamental discriminant. These computations go well beyond earlier results of Vogtmann and Scheutzow. We use the technique of homology of Voronoi complexes, and our computations recover the integral cohomology away from the primes 2, 3. We observed exponential growth in the torsion subgroup of H^2 as $D$ increases, and compared our data to bounds of Rohlfs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-12T18:57:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F75",
      "20J06",
      "11Y99"
    ],
    "keywords": [
      "imaginary quadratic fields",
      "computations",
      "integral cohomology away",
      "fundamental discriminant",
      "voronoi complexes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}