{
  "id": "1610.03552",
  "version": "v1",
  "published": "2016-10-11T22:32:49.000Z",
  "updated": "2016-10-11T22:32:49.000Z",
  "title": "Unlikely Intersections in Finite Characteristic",
  "authors": [
    "Ananth Shankar",
    "Jacob Tsimerman"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We present a heuristic argument based on Honda-Tate theory against many conjectures in `unlikely intersections' over the algebraic closure of a finite field; notably, we conjecture that every abelian variety of dimension 4 is isogenous to a Jacobian, contrary to a conjecture of Oort. Using methods of additive combinatorics, we are able to disprove a related conjecture of Oort where the ambient Shimura Variety is a power of the modular curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-11T22:32:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unlikely intersections",
      "finite characteristic",
      "conjecture",
      "ambient shimura variety",
      "honda-tate theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}