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truncated polynomial algebra

Journal of K-Theory (1)

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On the algebraic K-theory of truncated polynomial algebras in several variables
Vigleik Angeltveit, Teena Gerhardt, Michael A. Hill, Ayelet Lindenstrauss
Journal:

Journal of K-Theory / Volume 13 / Issue 1 / February 2014

Published online by Cambridge University Press:

18 February 2014, pp. 57-81

Print publication:

February 2014
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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 ℕn. 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 = 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.