{
  "id": "2001.10236",
  "version": "v1",
  "published": "2020-01-28T09:58:12.000Z",
  "updated": "2020-01-28T09:58:12.000Z",
  "title": "Duality for complexes of tori over a global field of positive characteristic",
  "authors": [
    "Cyril Demarche",
    "David Harari"
  ],
  "comment": "40 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "If K is a number field, arithmetic duality theorems for tori and complexes of tori over K are crucial to understand local-global principles for linear algebraic groups over K. When K is a global field of positive characteristic, we prove similar arithmetic duality theorems, including a Poitou-Tate exact sequence for Galois hypercohomology of complexes of tori. One of the main ingredients is Artin-Mazur-Milne duality theorem for fppf cohomology of finite flat commutative group schemes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-28T09:58:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E72",
      "11G20",
      "14F20",
      "14H25"
    ],
    "keywords": [
      "global field",
      "positive characteristic",
      "finite flat commutative group schemes",
      "similar arithmetic duality theorems",
      "understand local-global principles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}