{
  "id": "1812.04425",
  "version": "v1",
  "published": "2018-12-11T14:27:49.000Z",
  "updated": "2018-12-11T14:27:49.000Z",
  "title": "Rings of modular forms and a splitting of $TMF_0(7)$",
  "authors": [
    "Lennart Meier",
    "Viktoriya Ozornova"
  ],
  "comment": "62 pages; one appendix joint with Martin Olbermann",
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "Among topological modular forms with level structure, $TMF_0(7)$ at the prime $3$ is the first example that had not been understood yet. We provide a splitting of $TMF_0(7)$ at the prime 3 as $TMF$-module into two shifted copies of $TMF$ and two shifted copies of $TMF_1(2)$. This gives evidence to a much more general splitting conjecture. Along the way, we develop several new results on the algebraic side. For example, we show the normality of rings of modular forms of level $n$ and introduce cubical versions of moduli stacks of elliptic curves with level structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-11T14:27:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N34",
      "55P42",
      "14J15",
      "11F11",
      "14D23"
    ],
    "keywords": [
      "level structure",
      "shifted copies",
      "elliptic curves",
      "topological modular forms",
      "general splitting conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}