#### Volume 20, issue 2 (2020)

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On the Brun spectral sequence for topological Hochschild homology

### Eva Höning

Algebraic & Geometric Topology 20 (2020) 817–863
##### Abstract

We generalize a spectral sequence of Brun for the computation of topological Hochschild homology. The generalized version computes the $E$–homology of $THH\left(A;B\right)$, 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 $B{\wedge }_{A}B\phantom{\rule{-0.17em}{0ex}}$. 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.

##### Keywords
topological Hochschild homology, multiplicative spectral sequences, connective complex $K$–theory
##### Mathematical Subject Classification 2010
Primary: 19D55, 55P42, 55T99