{
  "id": "1311.1421",
  "version": "v3",
  "published": "2013-11-06T15:35:31.000Z",
  "updated": "2015-10-29T14:06:15.000Z",
  "title": "Multiplicative differential algebraic K-theory and applications",
  "authors": [
    "Ulrich Bunke",
    "Georg Tamme"
  ],
  "comment": "v1:28 pages, v2:revised version, v3:references updated, changed numbering to match published version. To appear in Annals of K-Theory",
  "categories": [
    "math.NT",
    "math.AG",
    "math.KT"
  ],
  "abstract": "We construct a version of Beilinson's regulator as a map of sheaves of commutative ring spectra and use it to define a multiplicative variant of differential algebraic K-theory. We use this theory to give an interpretation of Bloch's construction of K_3-classes and the relation with dilogarithms. Furthermore, we provide a relation to Arakelov theory via the arithmetic degree of metrized line bundles, and we give a proof of the formality of the algebraic K-theory of number rings.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-22T08:12:07.000Z",
      "comment": "v1:28 pages, v2:revised version",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-10-29T14:06:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiplicative differential algebraic k-theory",
      "applications",
      "metrized line bundles",
      "arithmetic degree",
      "beilinsons regulator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.1421B"
    }
  }
}