{
  "id": "1811.00604",
  "version": "v1",
  "published": "2018-11-01T19:35:48.000Z",
  "updated": "2018-11-01T19:35:48.000Z",
  "title": "Newton polygon stratification of the Torelli locus in PEL-type Shimura varieties",
  "authors": [
    "Wanlin Li",
    "Elena Mantovan",
    "Rachel Pries",
    "Yunqing Tang"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo $p$ reduction of certain PEL-type Shimura varieties. We develop a clutching method to show that the intersection of the Torelli locus with some Newton polygon strata is non-empty and has the expected codimension. This yields results about the Newton polygon stratification of Hurwitz spaces of cyclic covers of the projective line. The clutching method allows us to guarantee the existence of a smooth curve whose Newton polygon is the amalgamate sum of two other Newton polygons, under certain compatibility conditions. As an application, we produce infinitely many new examples of Newton polygons that occur for Jacobians of smooth curves in characteristic $p$. Most of these arise in inductive systems which demonstrate unlikely intersections of the Torelli locus with the Newton polygon stratification. As another application, for the PEL-type Shimura varieties associated to the twenty special families of cyclic covers of the projective line found by Moonen, we prove that all Newton polygon strata intersect the open Torelli locus (assuming $p$ sufficiently large for certain supersingular cases).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-01T19:35:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "11G20",
      "11M38",
      "14G10",
      "14G35",
      "11G10",
      "14H10",
      "14H30",
      "14H40",
      "14K10"
    ],
    "keywords": [
      "newton polygon stratification",
      "pel-type shimura varieties",
      "cyclic covers",
      "smooth curve",
      "newton polygon strata intersect"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}