{
  "id": "1410.2343",
  "version": "v1",
  "published": "2014-10-09T03:11:12.000Z",
  "updated": "2014-10-09T03:11:12.000Z",
  "title": "On Tate conjecture for the special fibers of some unitary Shimura varieties",
  "authors": [
    "David Helm",
    "Yichao Tian",
    "Liang Xiao"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $F$ be a totally real field in which a fixed prime $p$ is inert, and let $E$ be a CM extension of $F$ in which $p$ splits. We fix two positive integers $r,s \\in \\mathbb N$. We investigate the Tate conjecture on the special fiber of $G(U(r,s) \\times U(s,r))$-Shimura variety. We construct cycles which we conjecture to generate the Tate classes and verify our conjecture in the case of $G(U(1,s) \\times U(s,1))$. We also discuss the general conjecture regarding special cycles on the special fibers of unitary Shimura varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-09T03:11:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14G35",
      "14C25"
    ],
    "keywords": [
      "shimura variety",
      "unitary shimura varieties",
      "special fiber",
      "tate conjecture",
      "general conjecture regarding special cycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.2343H"
    }
  }
}