{
  "id": "1101.1866",
  "version": "v4",
  "published": "2011-01-10T16:14:00.000Z",
  "updated": "2015-04-06T01:28:28.000Z",
  "title": "On the algebraic K-theory of Witt vectors of finite length",
  "authors": [
    "Vigleik Angeltveit"
  ],
  "comment": "Major revision",
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "Let k be a perfect field of characteristic p and let $W_n(k)$ denote the p-typical Witt vectors of length n. For example, $W_n(\\mathbb{F}_p)=\\mathbb{Z}/p^n$. We study the algebraic K-theory of $W_n(k)$, and prove that $K(W_n(k))$ satisfies \"Galois descent\". We also compute the K-groups through a range of degrees, and show that the first p-torsion element in the stable homotopy groups of spheres is detected in $K_{2p-3}(W_n(k))$ for all $n \\geq 2$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-07-11T00:19:02.000Z",
      "abstract": "Let k be a perfect field of characteristic p and let W_n(k) denote the p-typical Witt vectors of length n. For example, W_n(F_p)=Z/p^n. We study the algebraic K-theory of W_n(k), and prove that K(W_n(k)) satisfies \"Galois descent\". We also compute the K-groups through a range of degrees, and show that the first p-torsion element in the stable homotopy groups of spheres is detected in K_{2p-3}(W_n(k)) for all n >=2.",
      "comment": "Major changes: Generalized from Z/p^n to length n Witt vectors over any perfect field of characteristic p. Added \"Galois descent\"",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-04-06T01:28:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19D55",
      "55T25"
    ],
    "keywords": [
      "algebraic k-theory",
      "finite length",
      "first p-torsion element",
      "galois descent",
      "p-typical witt vectors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}