{
  "id": "math/9811192",
  "version": "v1",
  "published": "1998-11-05T00:00:00.000Z",
  "updated": "1998-11-05T00:00:00.000Z",
  "title": "Towards regulator formulae for curves over number fields",
  "authors": [
    "Rob de Jeu"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "In this paper we study the group K_{2n}^{(n+1)}(F) where F is the function field of a complete, smooth, geometrically irreducible curve C over a number field, assuming the Beilinson--Soul\\'e conjecture on weights. In particular, we compute the Beilinson regulator on a subgroup of K_{2n}^{(n+1)}(F), using the complexes constructed in previous work by the author. We study the boundary map in the localization sequence for n = 3 (the case n = 2 was done in a previous paper). We combine our results with some results of Goncharov in order to obtain a complete description of the image of the regulator map on K_4^{(3)}(C) and K_6^{(4)}(C), independent of any conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-11-05T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "number field",
      "regulator formulae",
      "function field",
      "regulator map",
      "beilinson regulator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11192D"
    }
  }
}