{
  "id": "math/0310162",
  "version": "v1",
  "published": "2003-10-11T00:40:57.000Z",
  "updated": "2003-10-11T00:40:57.000Z",
  "title": "Algebraic cycles on Hilbert modular fourfolds and poles of L-functions",
  "authors": [
    "Dinakar Ramakrishnan"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "In this paper we give some evidence for the Tate (and Hodge) conjecture(s) for a class of Hilbert modular fourfolds X, whose connected components arise as arithmetic quotients of the fourfold product of the upper half plane by congruence subgroups \\Gamma of SL(2, O_K), where O_K denotes the ring of integers of a quartic, Galois, totally real number field K. The expected relationship to the orders of poles of the associated L-functions is verified for abelian extensions of \\Q. Also shown is the existence of homologically non-trivial cycles of codimension two which are not intersections of divisors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-11T00:40:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F41",
      "11G35",
      "14C25",
      "14G35"
    ],
    "keywords": [
      "hilbert modular fourfolds",
      "algebraic cycles",
      "l-functions",
      "upper half plane",
      "totally real number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10162R"
    }
  }
}