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

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

2008-09-21

arxiv.org/abs/0809.3544v2

J. Topol. 2 (2009), 277-294

Mathematics

Algebraic Topology

Journal of Topology (to appear)

Scientific paper

10.1112/jtopol/jtp011

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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