Localization for THH(ku) and the topological Hochschild and cyclic   homology of Waldhausen categories
  We prove a conjecture of Hesselholt and Ausoni-Rognes, establishing localization cofiber sequences of spectra for THH(ku) and TC(ku). These sequences support Hesselholt's view of the map l to ku as a "tamely ramified" extension of ring spectra, and validate the hypotheses necessary for Ausoni's simplified computation of V(1)_* K(KU).   In order to make sense of the relative term THH(ku|KU) in the cofiber sequence and prove these results, we develop a theory of THH and TC of Waldhausen categories and prove the analogues of Waldhausen's theorems for K-theory. We resolve the longstanding confusion about localization sequences in THH and TC, and establish a specialized devissage theorem. 
Andrew J. Blumberg, Michael A. Mandell
math.KT math.AT