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arXiv · 0809.3544

On the K-theory of truncated polynomial algebras over the integers

Vigleik Angeltveit·Teena Gerhardt·Lars Hesselholt
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Abstract

We show that the K_{2i}(Z[x]/(x^m),(x)) is finite of order (mi)!(i!)^{m-2} and that K_{2i+1}(Z[x]/(x^m),(x)) is free abelian of rank m-1. This is accomplished by showing that the equivariant homotopy groups of the topological Hochschild spectrum THH(Z) are finite, in odd degrees, and free abelian, in even degrees, and by evaluating their orders and ranks, respectively.

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Vigleik Angeltveit, Teena Gerhardt, Lars Hesselholt. 2009-04-20. On the K-theory of truncated polynomial algebras over the integers. https://doi.org/10.1112/jtopol%2Fjtp011

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