{
  "id": "2011.07241",
  "version": "v1",
  "published": "2020-11-14T08:47:30.000Z",
  "updated": "2020-11-14T08:47:30.000Z",
  "title": "Eisenstein cocycles in motivic cohomology",
  "authors": [
    "Romyar Sharifi",
    "Akshay Venkatesh"
  ],
  "comment": "86 pages",
  "categories": [
    "math.NT",
    "math.AG",
    "math.KT"
  ],
  "abstract": "Several authors have studied homomorphisms from first homology groups of modular curves to the second K-group of a cyclotomic ring or a modular curve X. These maps send Manin symbols in the homology groups to Steinberg symbols of cyclotomic or Siegel units. We give a new construction of these maps and a direct proof of their Hecke equivariance, analogous to the construction of Siegel units using the universal elliptic curve. Our main tool is a 1-cocycle from GL_2(Z) to the second K-group of the function field of a suitable group scheme over X, from which the maps of interest arise by specialization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-14T08:47:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F25",
      "11F75",
      "11G18",
      "14F42",
      "19E15",
      "19F15"
    ],
    "keywords": [
      "motivic cohomology",
      "eisenstein cocycles",
      "modular curve",
      "siegel units",
      "second k-group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 86,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}