{
  "id": "2312.12542",
  "version": "v1",
  "published": "2023-12-19T19:23:25.000Z",
  "updated": "2023-12-19T19:23:25.000Z",
  "title": "Modular functoriality in the Local Langlands Correspondence",
  "authors": [
    "Tony Feng"
  ],
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We develop a theory of Smith-Treumann localization and relative parity sheaves in the context of Fargues-Scholze's Geometrization of the Local Langlands Correspondence. We then apply this theory to prove some conjectures of Treumann-Venkatesh concerning mod-$\\ell$ Local Langlands functoriality between a reductive group $G$ and its fixed subgroup under an order $\\ell$ automorphism. As another application, we calculate the Fargues-Scholze parameters of mod-$\\ell$ Howe-unramified toral representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-19T19:23:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local langlands correspondence",
      "modular functoriality",
      "local langlands functoriality",
      "fargues-scholzes geometrization",
      "smith-treumann localization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}