On the Brun spectral sequence for topological Hochschild homology

Abstract

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 $A$-algebra. The input of the spectral sequence are the topological Hochschild homology groups of $B$ with coefficients in the $E$-homology groups of $B{\wedge }_{A}B$. The mod $p$ and $v_1$ 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.

References in corpus (3)

• Multiplicative structures on homotopy spectral sequences II
• The topological Hochschild homology of algebraic $K$-theory of finite fields
• Multiplicative structures on homotopy spectral sequences I

Cited by in corpus (4)

• The topological Hochschild homology of algebraic $K$-theory of finite fields
• Topological Hochschild homology of truncated Brown-Peterson spectra I
• Splittings and calculational techniques for higher THH
• Whitehead Filtrations for Computations in Topological Hochschild Homology