{
  "id": "1909.05734",
  "version": "v1",
  "published": "2019-09-12T14:55:31.000Z",
  "updated": "2019-09-12T14:55:31.000Z",
  "title": "Ramification of étale path torsors and harmonic analysis on graphs",
  "authors": [
    "L. Alexander Betts",
    "Netan Dogra"
  ],
  "comment": "119 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the Galois action on paths in the $\\mathbb{Q}_\\ell$-pro-unipotent \\'etale fundamental groupoid of a hyperbolic curve $X$ over a $p$-adic field with $\\ell\\neq p$. We prove an Oda--Tamagawa-type criterion for the existence of a Galois-invariant path in terms of the reduction of $X$, as well as an anabelian reconstruction result determining the stable reduction type of $X$ in terms of its fundamental groupoid. We give an explicit combinatorial description of the non-abelian Kummer map of $X$ in arbitrary depth, and deduce consequences for the non-abelian Chabauty method for affine hyperbolic curves and for explicit quadratic Chabauty.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-12T14:55:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic analysis",
      "path torsors",
      "ramification",
      "pro-unipotent etale fundamental groupoid",
      "affine hyperbolic curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 119,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}