### 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.

Bjørn Ian Dundas <dundas@math.uib.no>

Harald Øyen Kittang <harald.kittang@gmail.com>