{
  "id": "2009.05827",
  "version": "v1",
  "published": "2020-09-12T17:04:56.000Z",
  "updated": "2020-09-12T17:04:56.000Z",
  "title": "Algebraic $K$-theory of $\\text{THH}(\\mathbb{F}_p)$",
  "authors": [
    "Haldun Özgür Bayındır",
    "Tasos Moulinos"
  ],
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "In this work we study the $E_{\\infty}$-ring $\\text{THH}(\\mathbb{F}_p)$ from various perspectives. Following an identification at the level of $E_2$-algebras of $\\text{THH}(\\mathbb{F}_p)$ with $\\mathbb{F}_p[\\Omega S^3]$, the group ring of the $E_1$-group $\\Omega S^3$ over $\\mathbb{F}_p$, we use trace methods to compute its algebraic $K$-theory. We also show that as an $E_2$ $H\\mathbb{F}_p$-ring, $\\text{THH}(\\mathbb{F}_p)$ is uniquely determined by its homotopy groups. These results hold in fact for $\\text{THH}(k)$, where $k$ is any perfect field of characteristic $p$. Along the way we expand on some of the methods used by Hesselholt-Madsen and later by Speirs to develop certain tools to study the THH of graded ring spectra and the algebraic $K$-theory of formal DGAs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-12T17:04:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P99",
      "19D99"
    ],
    "keywords": [
      "formal dgas",
      "trace methods",
      "homotopy groups",
      "results hold",
      "perfect field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}