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.

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)