{
  "id": "2109.06581",
  "version": "v1",
  "published": "2021-09-14T11:05:25.000Z",
  "updated": "2021-09-14T11:05:25.000Z",
  "title": "Stabilization of the trace formula for metaplectic groups",
  "authors": [
    "Wen-Wei Li"
  ],
  "comment": "322 pages, with an index",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "We stabilize the full Arthur-Selberg trace formula for the metaplectic covering of symplectic groups over a number field. This provides a decomposition of the invariant trace formula for metaplectic groups, which encodes information about the genuine $L^2$-automorphic spectrum, into a linear combination of stable trace formulas of products of split odd orthogonal groups via endoscopic transfer. By adapting the strategies of Arthur and Moeglin-Waldspurger from the linear case, the proof is built on a long induction process that mixes up local and global, geometric and spectral data. As a by-product, we also stabilize the local trace formula for metaplectic groups over any local field of characteristic zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-14T11:05:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F72",
      "11F27",
      "11F70"
    ],
    "keywords": [
      "metaplectic groups",
      "stabilization",
      "full arthur-selberg trace formula",
      "split odd orthogonal groups",
      "local trace formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 322,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}