{
  "id": "2410.06217",
  "version": "v2",
  "published": "2024-10-08T17:24:22.000Z",
  "updated": "2024-12-03T01:06:14.000Z",
  "title": "On Brauer groups of tame stacks",
  "authors": [
    "Niven Achenjang"
  ],
  "comment": "57 pages, including ~11 pages of examples at the end. Comments are very welcome! v2: added some new results about Brauer groups of proper stacky curves (Section 7.2)",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We develop some general tools for computing the Brauer group of a tame algebraic stack $\\mathscr X$ by studying the difference between it and the Brauer group of the coarse space $X$ of $\\mathscr X$. It is our hope that these tools will be used to simplify future computations of Brauer groups of stacks. Informally, we show that $\\operatorname{Br}\\mathscr X$ is often built from $\\operatorname{Br} X$ and \"information about the Picard groups of the fibers of $\\mathscr X\\to X$''. Along these lines, we compute, for example, the Brauer group of the moduli stack $\\mathscr Y(1)_S$ of elliptic curves, over any regular noetherian $\\mathbb Z[1/2]$-scheme $S$ as well as the Brauer groups of (many) stacky curves (allowing generic stabilizers) over algebraically closed fields.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-12-03T01:06:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F22",
      "14D23",
      "14A20"
    ],
    "keywords": [
      "brauer group",
      "tame stacks",
      "tame algebraic stack",
      "coarse space",
      "general tools"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}