A relative spectral sequence for topological Hochschild homology of spectra

Abstract: In the situation where we have a sequence of two spectrum exten-sions, we describe a spectral sequence converging to the topological Hochschild homology of the top spectrum over the base spectrum, in terms of invariants of the intermediate extensions. The main application is to the case of topo-logical Hochschild homology of a ring extension, where the base spectrum is taken to be the sphere spectrum. We get a spectral sequence starting with ap-propriate algebraic Tor groups of the topological Hochschild homology groups of a ring, converging to the topological Hochschild homology of an algebra over it. AMS Subject Classification: 19D55 (16E40, 19D50, 55T99)