Integral excision for K-Theory

Abstract

If A is a homotopy cartesian square of ring spectra satisfy- ing connectivity hypotheses, then the cube induced by Good- willie's integral cyclotomic trace K(A)→T C(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. © 2013, International Press.