On the algebraic <i>K</i>-theory of truncated polynomial algebras in several variables

Abstract

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 ℕ n . If the characteristic of k does not divide any of the a i we compute the K -groups explicitly. We also compute the K -groups modulo torsion for k = ℤ. 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.