## Abstract

We consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables,. This naturally leads to a new generalization of the big Witt vectors. If k is a perfect field of positive characteristic we describe the K-theory computation in terms of a cube of these Witt vectors on â"•^{n}. If the characteristic of k does not divide any of the ai we compute the K-groups explicitly. We also compute the K-groups modulo torsion for k = â" To understand this K-theory spectrum we use the cyclotomic trace map to topological cyclic homology, and write as the iterated homotopy cofiber of an n-cube of spectra, each of which is easier to understand.

Original language | English |
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Pages (from-to) | 57-81 |

Number of pages | 25 |

Journal | Journal of K-Theory |

Volume | 13 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 2014 |