On the Brun spectral sequence for topological Hochschild homology

We generalize a spectral sequence of Brun for the computation of topological Hochschild homology. The generalized version computes the E-homology of THH(A;B), where E is a ring spectrum, A is a commutative S-algebra and B is a connective commutative Aalgebra. The input of the spectral sequence are the topological Hochschild homology groups of B with coefficients in the E-homology groups of B ∧A B. The mod p and v1 topological Hochschild homology of connective complex K-theory has been computed by Ausoni and later again by Rognes, Sagave and Schlichtkrull. We present an alternative, short computation using the generalized Brun spectral sequence.