Integral Excision for K-Theory
Algebraic Topology
2022-08-24 v1 Algebraic Geometry
Category Theory
K-Theory and Homology
Rings and Algebras
Abstract
If A is a homotopy cartesian square of ring spectra satisfying connectivity hypotheses, then the cube induced by Goodwillie's integral cyclotomic trace from K(A) to 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
Cite
@article{arxiv.1009.3044,
title = {Integral Excision for K-Theory},
author = {Bjørn Ian Dundas and Harald Øyen Kittang},
journal= {arXiv preprint arXiv:1009.3044},
year = {2022}
}
Comments
21 pages