{
  "id": "math/0203114",
  "version": "v3",
  "published": "2002-03-12T20:30:28.000Z",
  "updated": "2003-11-06T16:28:06.000Z",
  "title": "Residues and tame symbols on toroidal varieties",
  "authors": [
    "Ivan Soprounov"
  ],
  "comment": "26 pages, minor changes, title changed, new introduction, references added",
  "journal": "Compositio Math. 140 (2004) no. 6, 1593--1613",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "We introduce a new approach to the study of a system of algebraic equations in the algebraic torus whose Newton polytopes have sufficiently general relative positions. Our method is based on the theory of Parshin's residues and tame symbols on toroidal varieties. It provides a uniform algebraic explanation of the recent result of Khovanskii on the product of the roots of such systems and the Gel'fond--Khovanskii result on the sum of the values of a Laurent polynomial over the roots of such systems, and extends them to the case of an algebraically closed field of arbitrary characteristic.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-11-06T16:28:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "52B20"
    ],
    "keywords": [
      "toroidal varieties",
      "tame symbols",
      "uniform algebraic explanation",
      "newton polytopes",
      "arbitrary characteristic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......3114S"
    }
  }
}