On the K-theory and topological cyclic homology of smooth schemes over a discrete valuation ring (with Thomas Geisser)

Let V be a discrete valuation ring of mixed characteristic (0,p) and let X be a smooth and proper scheme over V. We show that with Z/pv-coefficients, the cyclotomic trace induces an isomorphism of the Dwyer-Friedlander etale K-theory of X and the topological cyclic homology of X.

Thomas Geisser <geisser@math.usc.edu>
Lars Hesselholt <larsh@math.mit.edu>