{
  "id": "2208.06921",
  "version": "v1",
  "published": "2022-08-14T21:02:36.000Z",
  "updated": "2022-08-14T21:02:36.000Z",
  "title": "Level compatibility in Sharifi's conjecture",
  "authors": [
    "Emmanuel Lecouturier",
    "Jun Wang"
  ],
  "comment": "Comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Sharifi has constructed a map from the first homology of the modular curve $X_1(M)$ to the $K$-group $K_2(\\mathbf{Z}[\\zeta_M, \\frac{1}{M}])$, where $\\zeta_M$ is a primitive $M$th root of unity. We study how these maps relate when $M$ varies. Our method relies on the techniques developed by Sharifi and Venkatesh.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-14T21:02:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sharifis conjecture",
      "level compatibility",
      "method relies",
      "modular curve",
      "th root"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}