{
  "id": "1705.03786",
  "version": "v1",
  "published": "2017-05-10T14:14:49.000Z",
  "updated": "2017-05-10T14:14:49.000Z",
  "title": "Cohomology and overconvergence for representations of powers of Galois groups",
  "authors": [
    "Aprameyo Pal",
    "Gergely Zábrádi"
  ],
  "comment": "53 pages, submitted",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We show that the Galois cohomology groups of $p$-adic representations of a direct power of $\\operatorname{Gal}(\\overline{\\mathbb{Q}_p}/\\mathbb{Q}_p)$ can be computed via the generalization of Herr's complex to multivariable $(\\varphi,\\Gamma)$-modules. Using Tate duality and a pairing for multivariable $(\\varphi,\\Gamma)$-modules we extend this to analogues of the Iwasawa cohomology. We show that all $p$-adic representations of a direct power of $\\operatorname{Gal}(\\overline{\\mathbb{Q}_p}/\\mathbb{Q}_p)$ are overconvergent and, moreover, passing to overconvergent multivariable $(\\varphi,\\Gamma)$-modules is an equivalence of categories. Finally, we prove that the overconvergent Herr complex also computes the Galois cohomology groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-10T14:14:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois groups",
      "galois cohomology groups",
      "adic representations",
      "direct power",
      "overconvergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}