{
  "id": "2410.15598",
  "version": "v1",
  "published": "2024-10-21T02:45:42.000Z",
  "updated": "2024-10-21T02:45:42.000Z",
  "title": "Rost injectivity for classical groups over function fields of curves over local fields",
  "authors": [
    "R. Parimala",
    "V. Suresh"
  ],
  "comment": "23 pages",
  "categories": [
    "math.NT",
    "math.AG",
    "math.RA"
  ],
  "abstract": "Let F be a complete discretely valued field with residue field a global field or a local field with no real orderings. Let G be an absolutely simple simply connected group of outer type A_n. If 2 and the index of the underlying algebra of G are coprime to the characteristic of the residue field of F, then we prove that the Rost invariant map from the first Galois cohomology set of G to the degree three Galois cohomology group is injective. Let L be the function field of a curve over a local field K and G an absolutely simple simply connected linear algebraic group over L of classical type. Suppose that the characteristic of the residue field of K is a good prime for G. As a consequence of our result and some known results we conclude that the Rost invariant of G is injective.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-21T02:45:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E57",
      "11E39"
    ],
    "keywords": [
      "local field",
      "function field",
      "rost injectivity",
      "connected linear algebraic group",
      "classical groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}