{
  "id": "2103.16006",
  "version": "v1",
  "published": "2021-03-30T00:39:14.000Z",
  "updated": "2021-03-30T00:39:14.000Z",
  "title": "On the $C_p$-equivariant dual Steenrod algebra",
  "authors": [
    "Krishanu Sankar",
    "Dylan Wilson"
  ],
  "comment": "15 pages, comments welcome!",
  "categories": [
    "math.AT"
  ],
  "abstract": "We compute the $C_p$-equivariant dual Steenrod algebras associated to the constant Mackey functors $\\underline{\\mathbb{F}}_p$ and $\\underline{\\mathbb{Z}}_{(p)}$, as $\\underline{\\mathbb{Z}}_{(p)}$-modules. The $C_p$-spectrum $\\underline{\\mathbb{F}}_p \\otimes \\underline{\\mathbb{F}}_p$ is not a direct sum of $RO(C_p)$-graded suspensions of $\\underline{\\mathbb{F}}_p$ when $p$ is odd, in contrast with the classical and $C_2$-equivariant dual Steenrod algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-30T00:39:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equivariant dual steenrod algebra",
      "constant mackey functors",
      "direct sum",
      "graded suspensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}