On the algebraic K-theory of Z/p^n

Details On the algebraic K-theory of Z/p^n On the algebraic K-theory of Z/p^n

2011-01-10

arxiv.org/abs/1101.1866v2

Mathematics

Algebraic Topology

Minor changes, submitted

Scientific paper

We study the algebraic K-theory groups of the ring Z/p^n using the cyclotomic trace map to the topological cyclic homology spectrum TC(Z/p^n). We prove that K_q(Z/p^n) is finite for all n \geq 2 and q \geq 1 and that the order satisfies |K_{2i-1}(Z/p^n)|/|K_{2i-2}(Z/p^n)|=p^{(n-1)i}(p^i-1)$ for all i \geq 2. We also determine the group K_q(Z/p^n) for all n \geq 2 and q \leq 2p-2. We approach TC(Z/p^n) by filtering Z/p^n by powers of p and studying several spectral sequences related to this filtration.

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