{
  "id": "2104.06974",
  "version": "v1",
  "published": "2021-04-14T16:57:15.000Z",
  "updated": "2021-04-14T16:57:15.000Z",
  "title": "On the local constancy of certain mod $p$ Galois representations",
  "authors": [
    "Abhik Ganguli",
    "Suneel Kumar"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this article we study local constancy of the mod $p$ reduction of certain $2$-dimensional crystalline representations of $\\mathrm{Gal}\\left(\\bar{\\mathbb{Q}}_p/\\mathbb{Q}_p\\right)$ using the mod $p$ local Langlands correspondence. We prove local constancy in the weight space by giving an explicit lower bound on the local constancy radius centered around weights going up to $(p-1)^{2} +3$ and the slope fixed in $(0, \\ p-1)$ satisfying certain constraints. We establish the lower bound by determining explicitly the mod $p$ reductions at nearby weights and applying a local constancy result of Berger.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-14T16:57:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois representations",
      "study local constancy",
      "dimensional crystalline representations",
      "explicit lower bound",
      "local constancy result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}