Integral excision for K-theory, by Bjørn Ian Dundas and Harald Øyen Kittang

Given a homotopy cartesian square of ring spectra satisfying connectivity hypotheses, the cube induced by Goodwillie’s integral cyclotomic trace is homotopy cartesian. In other words, the homotopy fiber of the cyclotomic trace satisfies excision under "closed embeddings" of ring spectra. This was previously known after p-completion by work of Geisser and Hesselholt, and the current authors. Earlier Cortinas had proven the corresponding rational statement connecting algebraic K-theory and cyclic homology. In this paper we glue these results together to give an integral statement. This is not straight forward since it involves a mixture of rationalization and homotopy limits, which are usually hard to reconcile. The method of proof is to fracture the obstruction into pieces where the size of the torsion is controlled. This also has direct applications to similar situations involving periodic cyclic homology.

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Bjørn Ian Dundas <dundas@math.uib.no>
Harald Øyen Kittang <harald.kittang@gmail.com>