{
  "id": "2203.09651",
  "version": "v1",
  "published": "2022-03-17T23:19:38.000Z",
  "updated": "2022-03-17T23:19:38.000Z",
  "title": "Local-global principles for hermitian spaces over semi-global fields",
  "authors": [
    "Jayanth Guhan",
    "V. Suresh"
  ],
  "categories": [
    "math.AG",
    "math.AC",
    "math.NT",
    "math.RA"
  ],
  "abstract": "Let $K$ be a complete discrete valued field with residue field $k$ and $F$ the function field of a curve over $K$. Let $A \\in {}_2Br(F)$ be a central simple algebra with an involution $\\sigma$ of any kind and $F_0 =F^{\\sigma}$. Let $h$ be an hermitian space over $(A, \\sigma)$ and $G = SU(A, \\sigma, h)$ if $\\sigma$ is of first kind and $G = U(A, \\sigma, h)$ if $\\sigma$ is of second kind. Suppose that $\\text{char}(k) \\neq 2$ and ind$(A)\\leq 4$. Then we prove that projective homogeneous spaces under $G$ over $F_0$ satisfy a local-global principle for rational points with respect to discrete valuations of $F$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-17T23:19:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local-global principle",
      "hermitian space",
      "semi-global fields",
      "central simple algebra",
      "complete discrete valued field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}