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On the algebraic K-theory of truncated polynomial algebras in several variables

Published online by Cambridge University Press:  18 February 2014

Vigleik Angeltveit ,
Teena Gerhardt ,
Michael A. Hill  and
Ayelet Lindenstrauss
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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 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.

Keywords

Algebraic K-theorytrace maptruncated polynomial algebra19D5555P42

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Type
Research Article
Information
Journal of K-Theory , Volume 13 , Issue 1 , February 2014 , pp. 57 - 81
Copyright
Copyright © ISOPP 2014 

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References

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