Excision for K-theory of connective ring spectra

Details Excision for K-theory of connective ring spectra Excision for K-theory of connective ring spectra

2007-04-30

arxiv.org/abs/0704.3946v1

Mathematics

K-Theory and Homology

11 pages

Scientific paper

We extend Geisser and Hesselholt's result on ``bi-relative K-theory'' from discrete rings to connective ring spectra. That is, if $\mathcal A$ is a homotopy cartesian $n$-cube of ring spectra (satisfying connectivity hypotheses), then the $(n+1)$-cube induced by the cyclotomic trace $$K(\mathcal A)\to TC(\mathcal A)$$ is homotopy cartesian after profinite completion. In other words, the fiber of the profinitely completed cyclotomic trace satisfies excision.

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