{
  "id": "1706.03387",
  "version": "v1",
  "published": "2017-06-11T18:23:16.000Z",
  "updated": "2017-06-11T18:23:16.000Z",
  "title": "Gerbe patching and a Mayer-Vietoris sequence over arithmetic curves",
  "authors": [
    "Bastian Haase"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We discuss patching techniques and local-global principles for gerbes over arithmetic curves. Our patching setup is that introduced by Harbater, Hartmann and Krashen. Our results for gerbes can be viewed as a 2-categorical analogue on their results for torsors. Along the way, we also discuss bitorsor patching and local-global principles for bitorsors. As an application of these results, we obtain a Mayer-Vietoris sequence with respect to patches for non-abelian hypercohomology sets with values in the crossed module G->Aut(G) for G a linear algebraic group. Using local-global principles for gerbes, we also prove local-global principles for points on homogeneous spaces under linear algebraic groups H that are special (e.g. SL_n and Sp_2n) for certain kind of stabilizers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-11T18:23:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H25",
      "18G50",
      "14M17"
    ],
    "keywords": [
      "mayer-vietoris sequence",
      "arithmetic curves",
      "local-global principles",
      "gerbe patching",
      "linear algebraic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}