Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories - Blumberg, Andrew J.; Mandell, Michael A. (Memoirs of the American Mathematical Society, 2020)
The authors develop a theory of THH and TC of Waldhausen categories and prove the analogues of Waldhausen's theorems for K-theory. They resolve the longstanding confusion about localization sequences in THH and TC, and establish a specialized dévissage theorem. As applications, the authors prove conjectures of Hesselholt and Ausoni-Rognes about localization cofiber sequences surrounding THH(ku), and more generally establish a framework for advancing the Rognes program for studying Waldhausen's chromatic filtration on A(*).