A relative spectral sequence for topological Hochschild homology of spectra

In the situation where we have a sequence of two spectrum extensions, we de scribe a spectral sequence converging to the topological Hochschild homolog y of the top spectrum over the base spectrum, in terms of invariants of the intermediate extensions. The main application is to the case of topologica l Hochschild homology of a ring extension, when the base spectrum is taken to be the sphere spectrum. We get a spectral sequence starting with appropr iate algebraic Tor groups of the topological Hochschild homology groups of a ring, converging to the topological Hochschild homology of an algebra ove r it. (C) 2000 Elsevier Science B.V. All rights reserved. MSC. 19D55; 16E40 ; 19D50; 55T99.