On the Brun spectral sequence for topological Hochschild homology

Höning, Eva

doi:10.2140/agt.2020.20.817

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On the Brun spectral sequence for topological Hochschild homology

Eva Höning

Algebraic & Geometric Topology 20 (2020) 817–863

DOI: 10.2140/agt.2020.20.817

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 $B \land_{A} B$ . 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.

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Keywords

topological Hochschild homology, multiplicative spectral sequences, connective complex $K$–theory

Mathematical Subject Classification 2010

Primary: 19D55, 55P42, 55T99

References

Publication

Received: 27 August 2018

Revised: 6 August 2019

Accepted: 15 August 2019

Published: 23 April 2020

Authors

Eva Höning
Fachbereich Mathematik der Universität Hamburg Hamburg Germany

Volume 20, issue 2 (2020)