{
  "id": "2201.12780",
  "version": "v1",
  "published": "2022-01-30T10:28:03.000Z",
  "updated": "2022-01-30T10:28:03.000Z",
  "title": "Period -Index problem for hyperelliptic curves",
  "authors": [
    "J. N. Iyer",
    "R. Parimala"
  ],
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let $C$ be a smooth projective curve of genus 2 over a number field $k$ with a rational point. We prove that the index and exponent coincide for elements in the 2-torsion of $\\Sha(Br(C))$. In the appendix, an isomorphism of the moduli space of rank 2 stable vector bundles with odd determinant on a smooth projective hyperelliptic curve $C$ of genus $g$ with a rational point over any field of characteristic not two with the Grassmannian of $(g-1)$-dimensional linear subspaces in the base locus of a certain pencil of quadrics is established, making a result of (\\cite{De-Ra}) rational. We establish a twisted version of this isomorphism and we derive as a consequence a weak Hasse principle for the smooth intersection $X$ of two quadrics in ${\\mathbb P}^5$ over a number field: if $X$ contains a line locally, then $X$ has a $k$-rational point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-30T10:28:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "index problem",
      "rational point",
      "number field",
      "weak hasse principle",
      "dimensional linear subspaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}