{
  "id": "1910.03164",
  "version": "v1",
  "published": "2019-10-08T01:54:02.000Z",
  "updated": "2019-10-08T01:54:02.000Z",
  "title": "Potential automorphy of $\\mathrm{GSpin}_{2n+1}$-valued Galois representations",
  "authors": [
    "Stefan Patrikis",
    "Shiang Tang"
  ],
  "comment": "comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove a potentially automorphy theorem for suitable Galois representations $\\Gamma_{F^+} \\to \\mathrm{GSpin}_{2n+1}(\\overline{\\mathbb{F}}_p)$ and $\\Gamma_{F^+} \\to \\mathrm{GSpin}_{2n+1}(\\overline{\\mathbb{Q}}_p)$, where $\\Gamma_{F^+}$ is the absolute Galois group of a totally real field $F^+$. We also prove results on solvable descent for $\\mathrm{GSp}_{2n}(\\mathbb{A}_{F^+})$ and use these to put representations $\\Gamma_{F^+} \\to \\mathrm{GSpin}_{2n+1}(\\overline{\\mathbb{Q}}_p)$ into compatible systems of $\\mathrm{GSpin}_{2n+1}(\\overline{\\mathbb{Q}}_{\\ell})$-valued representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-08T01:54:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11R39"
    ],
    "keywords": [
      "valued galois representations",
      "potential automorphy",
      "absolute galois group",
      "potentially automorphy theorem",
      "totally real field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}