{
  "id": "2209.07107",
  "version": "v1",
  "published": "2022-09-15T07:36:39.000Z",
  "updated": "2022-09-15T07:36:39.000Z",
  "title": "Quadratic Pairs on Azumaya Algebras over a Scheme",
  "authors": [
    "Philippe Gille",
    "Erhard Neher",
    "Cameron Roy Ruether"
  ],
  "categories": [
    "math.AG",
    "math.RA"
  ],
  "abstract": "We investigate quadratic pairs for Azumaya algebras with involutions over a base scheme S as defined by Calm{\\`e}s and Fasel, generalizing the case of quadratic pairs on central simple algebras over a field (Knus, Merkurjev, Rost, Tignol). We describe a cohomological obstruction for an Azumaya algebra over S with orthogonal involution to admit a quadratic pair. When S is affine this obstruction vanishes, however it is non-trivial in general. In particular, we construct explicit examples with non-trivial obstructions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-15T07:36:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic pair",
      "azumaya algebra",
      "central simple algebras",
      "construct explicit examples",
      "orthogonal involution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}