{
  "id": "2403.06724",
  "version": "v1",
  "published": "2024-03-11T13:44:41.000Z",
  "updated": "2024-03-11T13:44:41.000Z",
  "title": "A note on the Segal conjecture for large objects",
  "authors": [
    "Robert Burklund",
    "Vignesh Subramanian"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "The Segal conjecture for $C_p$ (as proved by Lin and Gunawardena) asserts that the canonical map from the $p$-complete sphere spectrum to the Tate construction for the trivial action of $C_p$ on the $p$-complete sphere spectrum is an isomorphism. In this article we extend the collection of spectra for which the canonical map $X \\to X^{tC_p}$ is known to be an isomorphism to include any $p$-complete, bounded below spectrum whose mod $p$ homology, viewed a module over the Steenrod algebra, is complete with respect to the maximal ideal $I \\subseteq \\mathcal{A}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-11T13:44:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "segal conjecture",
      "large objects",
      "complete sphere spectrum",
      "canonical map",
      "steenrod algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}