{
  "id": "2210.15994",
  "version": "v1",
  "published": "2022-10-28T08:54:26.000Z",
  "updated": "2022-10-28T08:54:26.000Z",
  "title": "Cohomology of the Morava stabilizer group through the duality resolution at $n=p=2$",
  "authors": [
    "Agnes Beaudry",
    "Irina Bobkova",
    "Paul G. Goerss",
    "Hans-Werner Henn",
    "Viet-Cuong Pham",
    "Vesna Stojanoska"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "We compute the continuous cohomology of the Morava stabilizer group with coefficients in Morava $E$-theory, $H^*(\\mathbb{G}_2, E_t)$, at $p=2$, for $0\\leq t < 12$, using the Algebraic Duality Spectral Sequence. Furthermore, in that same range, we compute the $d_3$-differentials in the homotopy fixed point spectral sequence for the $K(2)$-local sphere spectrum. These cohomology groups and differentials play a central role in $K(2)$-local stable homotopy theory, in particular for the analysis of the $K(2)$-local Picard group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-28T08:54:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "morava stabilizer group",
      "duality resolution",
      "cohomology",
      "algebraic duality spectral sequence",
      "homotopy fixed point spectral sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}