{
  "id": "2211.08470",
  "version": "v1",
  "published": "2022-11-15T19:47:58.000Z",
  "updated": "2022-11-15T19:47:58.000Z",
  "title": "V-vector Bundles On P-adic Fields And Sen Theory Via The Hodge-tate Stack",
  "authors": [
    "Johannes Anschütz",
    "Ben Heuer",
    "Arthur-César Le Bras"
  ],
  "comment": "29 pages, comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "We describe the category of continuous semilinear representations and their cohomology for the Galois group of a $p$-adic field $K$ with coefficients in a completed algebraic closure via vector bundles on the Hodge-Tate locus of the Cartier-Witt stack. This also gives a new perspective on classical Sen theory; for example it explains the appearance of an analogue of Colmez' period ring $B_{\\mathrm{Sen}}$ in a geometric way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-15T19:47:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S25",
      "11S20"
    ],
    "keywords": [
      "p-adic fields",
      "hodge-tate stack",
      "v-vector bundles",
      "continuous semilinear representations",
      "geometric way"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}