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

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 AB. 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.

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topological Hochschild homology, multiplicative spectral sequences, connective complex $K$–theory
Mathematical Subject Classification 2010
Primary: 19D55, 55P42, 55T99
Received: 27 August 2018
Revised: 6 August 2019
Accepted: 15 August 2019
Published: 23 April 2020
Eva Höning
Fachbereich Mathematik der Universität Hamburg