If A is a homotopy cartesian square of ring spectra satisfying connectivity hypotheses, then the cube induced by Goodwillie's integral cyclotomic trace K(A) → TC(A) is homotopy cartesian. In other words, the homotopy fiber of the cyclotomic trace satisfies excision.
The method of proof gives as a spin-off new proofs of some old results, as well as some new results, about periodic cyclic homology, and - more relevantly for our current application - the T-Tate spectrum of topological Hochschild homology, where T is the circle group.
Homology, Homotopy and Applications, Vol. 15 (2013), No. 1, pp.1-25.
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