Excision for K-theory of connective ring spectra

Bjørn Ian Dundas and Harald Øyen Kittang

We extend Geisser and Hesselholt's result on "bi-relative K-theory" from discrete rings to connective ring spectra. That is, if A is a homotopy cartesian n-cube of ring spectra (satisfying connectivity hypotheses), then the (n+1)-cube induced by the cyclotomic trace

K(A) → TC(A)

is homotopy cartesian after profinite completion. In other words, the fiber of the profinitely completed cyclotomic trace satisfies excision.

Homology, Homotopy and Applications, Vol. 10 (2008), No. 1, pp.29-39.

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