Homology, Homotopy and Applications
Volume 15 (2013)
Integral excision for $K$-theory
Pages: 1 – 25
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.
excision in algebraic $K$-theory, derived algebraic geometry, ring spectrum, cyclotomic trace
2010 Mathematics Subject Classification
13D15, 14A20, 19D55, 55P43