... suggestions on improving the exposition.1. Topological Hochschild homology and localization1.1. This section contains the construction of TRn(A|K; p). The mainresult is the localization sequence of ... THH(Nz·S·Cb(MA)q).Proof. We show that the assumptions of Proposition 1.5.1 are satisfied.The proof relies on Waldhausen’s approximation theorem, [48, Th. 1.6.7], butin a formulation due to Thomason, [46, ... Cb(A). The inclusion E→Cb (E) ofE asthe subcategory of complexes concentrated in degree zero, is an exact functor.The assumptions of the fibration Theorem 1.3.11 are satisfied for Cb (E) .Theorem...