{
  "id": "1407.5709",
  "version": "v1",
  "published": "2014-07-22T02:01:10.000Z",
  "updated": "2014-07-22T02:01:10.000Z",
  "title": "The Geometry of Hida Families II: $Λ$-adic $(\\varphi,Γ)$-modules and $Λ$-adic Hodge Theory",
  "authors": [
    "Bryden Cais"
  ],
  "comment": "This paper is a continuation of our previous paper \"The Geometry of Hida Families I: $\\Lambda$-adic de Rham cohomology\", and is a revised version of part of the paper arXiv:1209.0046",
  "categories": [
    "math.NT"
  ],
  "abstract": "We construct the $\\Lambda$-adic crystalline and Dieudonn\\'e analogues of Hida's ordinary $\\Lambda$-adic \\'etale cohomology, and employ integral $p$-adic Hodge theory to prove $\\Lambda$-adic comparison isomorphisms between these cohomologies and the $\\Lambda$-adic de Rham cohomology studied in the prequel to this paper as well as Hida's $\\Lambda$-adic \\'etale cohomology. As applications of our work, we provide a \"cohomological\" construction of the family of $(\\varphi,\\Gamma)$-modules attached to Hida's ordinary $\\Lambda$-adic \\'etale cohomology by the work of Dee, and we give a new and purely geometric proof of Hida's finitenes and control theorems. We also prove suitable $\\Lambda$-adic duality theorems for each of the cohomologies we construct.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-22T02:01:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F33",
      "11F67",
      "11G18",
      "11R23"
    ],
    "keywords": [
      "adic hodge theory",
      "adic etale cohomology",
      "hida families",
      "hidas ordinary",
      "adic comparison isomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.5709C"
    }
  }
}