{
  "id": "1909.07473",
  "version": "v1",
  "published": "2019-09-16T20:43:21.000Z",
  "updated": "2019-09-16T20:43:21.000Z",
  "title": "Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields",
  "authors": [
    "Ananth N. Shankar",
    "Arul Shankar",
    "Yunqing Tang",
    "Salim Tayou"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Given a K3 surface $X$ over a number field $K$, we prove that the set of primes of $K$ where the geometric Picard rank jumps is infinite, assuming that $X$ has everywhere potentially good reduction. The result is a special case of a more general one on exceptional classes for K3 type motives associated to GSpin Shimura varieties and several other applications are given. As a corollary, we give a new proof of the fact that $X_{\\overline{K}}$ has infinitely many rational curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-16T20:43:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14J28",
      "11G10"
    ],
    "keywords": [
      "number field",
      "k3 surface",
      "exceptional jumps",
      "geometric picard rank jumps",
      "k3 type motives"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}