{
  "id": "2205.04499",
  "version": "v1",
  "published": "2022-05-09T18:14:47.000Z",
  "updated": "2022-05-09T18:14:47.000Z",
  "title": "Cyclic base change of cuspidal automorphic representations over function fields",
  "authors": [
    "Gebhard Böckle",
    "Tony Feng",
    "Michael Harris",
    "Chandrashekhar Khare",
    "Jack A. Thorne"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $G$ be a split semi-simple group over a global function field $K$. Given a cuspidal automorphic representation $\\Pi$ of $G$ satisfying a technical hypothesis, we prove that for almost all primes $\\ell$, there is a cyclic base change lifting of $\\Pi$ along any $\\mathbb{Z}/\\ell\\mathbb{Z}$-extension of $K$. Our proof does not rely on any trace formulas; instead it is based on modularity lifting theorems, together with a Smith theory argument to obtain base change for residual representations. As an application, we also prove that for any split semisimple group $G$ over a local function field $F$, and almost all primes $\\ell$, any irreducible admissible representation of $G(F)$ admits a base change along any $\\mathbb{Z}/\\ell\\mathbb{Z}$-extension of $F$. Finally, we characterize local base change more explicitly for a class of representations called toral supercuspidal representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-09T18:14:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cuspidal automorphic representation",
      "cyclic base change",
      "split semi-simple group",
      "toral supercuspidal representations",
      "characterize local base change"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}