{
  "id": "2402.06620",
  "version": "v2",
  "published": "2024-02-09T18:53:09.000Z",
  "updated": "2024-12-19T14:36:00.000Z",
  "title": "The Brauer groups of moduli of genus three curves, abelian threefolds and plane curves",
  "authors": [
    "Andrea Di Lorenzo",
    "Roberto Pirisi"
  ],
  "comment": "Previous version contained a mistake: we now only compute the invariants up to degree two, which suffice to compute the Brauer group. We added a section showing that the Brauer group of the moduli stack of smooth genus three curves is isomorphic to the Brauer grouip of the moduli stack of three dimensional principally polarized abelian varieties",
  "categories": [
    "math.AG"
  ],
  "abstract": "We compute the $\\ell$-primary torsion of the Brauer group of the moduli stack of smooth curves of genus three over any field of characteristic different from two and the Brauer group of the moduli stacks of smooth plane curves of degree $d$ over any algebraically closed field of characteristic different from two, three and coprime to $d$. We achieve this result by computing the low degree cohomological invariants of these stacks. As a corollary we are additionally able to compute the $\\ell$-primary torsion of the Brauer group of the moduli stack of principally polarized abelian varieties of dimension three over any field of characteristic different from two.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-12-19T14:36:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F22",
      "14H10"
    ],
    "keywords": [
      "brauer group",
      "abelian threefolds",
      "moduli stack",
      "primary torsion",
      "smooth plane curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}