{
  "id": "2208.08325",
  "version": "v1",
  "published": "2022-08-17T14:48:57.000Z",
  "updated": "2022-08-17T14:48:57.000Z",
  "title": "Algebraic Cycles and values of Green's functions",
  "authors": [
    "Ramesh Sreekantan"
  ],
  "comment": "41 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We construct indecomposable cycles in the motivic cohomology group $H^3_{{\\mathcal M}}(A,{\\mathbb Q}(2))$ where $A$ is an Abelian surface over a number field or the function field of a base. When $A$ is the self product of the universal elliptic curve over a modular curve, these cycles can be used to prove algebraicity results for values of higher Green's functions, similar to a conjecture of Gross, Kohnen and Zagier. We formulate a conjecture which relates our work with the recent work of Bruinier-Ehlen-Yang on the conjecture of Gross-Kohnen-Zagier.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-17T14:48:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G15",
      "11G18",
      "14K22",
      "14C25",
      "14G35",
      "19E15"
    ],
    "keywords": [
      "algebraic cycles",
      "motivic cohomology group",
      "higher greens functions",
      "universal elliptic curve",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}