{
  "id": "2305.09595",
  "version": "v1",
  "published": "2023-05-16T16:50:43.000Z",
  "updated": "2023-05-16T16:50:43.000Z",
  "title": "Hecke operators for curves over non-archimedean local fields and related finite rings",
  "authors": [
    "Alexander Braverman",
    "David Kazhdan",
    "Alexander Polishchuk"
  ],
  "comment": "34 pages",
  "categories": [
    "math.NT",
    "math.AG",
    "math.RT"
  ],
  "abstract": "We study Hecke operators associated with curves over a non-archimedean local field $K$ and over the rings $O/{\\mathfrak m}^N$, where $O\\subset K$ is the ring of integers. Our main result is commutativity of a certain ``small\" local Hecke algebra over $O/{\\mathfrak m}^N$, associated with a connected split reductive group $G$ such that $[G,G]$ is simple and simpy connected. The proof uses a Hecke algebra associated with $G(K(\\!(t)\\!))$ and a global argument involving $G$-bundles on curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-16T16:50:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-archimedean local field",
      "related finite rings",
      "study hecke operators",
      "local hecke algebra",
      "connected split reductive group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}