{
  "id": "1503.07751",
  "version": "v1",
  "published": "2015-03-26T14:37:26.000Z",
  "updated": "2015-03-26T14:37:26.000Z",
  "title": "An arithmetic Lefschetz-Riemann-Roch theorem",
  "authors": [
    "Shun Tang"
  ],
  "comment": "51 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this article, we consider regular arithmetic schemes in the context of Arakelov geometry, endowed with an action of the diagonalisable group scheme associated to a finite cyclic group. For any equivariant and proper morphism of such arithmetic schemes, which is smooth over the generic fibre, we define a direct image map between corresponding higher equivariant arithmetic K-groups and we discuss its transitivity property. Then we use the localization sequence of higher arithmetic K-groups and the higher arithmetic concentration theorem developed in \\cite{T3} to prove an arithmetic Lefschetz-Riemann-Roch theorem. This theorem can be viewed as a generalization, to the higher equivariant arithmetic K-theory, of the fixed point formula of Lefschetz type proved by K. K\\\"{o}hler and D. Roessler in \\cite{KR1}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-26T14:37:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C40",
      "14G40",
      "14L30",
      "19E08",
      "58J52"
    ],
    "keywords": [
      "arithmetic lefschetz-riemann-roch theorem",
      "arithmetic concentration theorem",
      "higher equivariant arithmetic k-theory",
      "arithmetic schemes",
      "corresponding higher equivariant arithmetic k-groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150307751T"
    }
  }
}