On the Brun spectral sequence for topological Hochschild homology

Höning, Eva¹

¹Fachbereich Mathematik der Universität Hamburg, Hamburg, Germany

Algebraic and Geometric Topology, Tome 20 (2020) no. 2, pp. 817-863

Résumé

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.

Détail

DOI : 10.2140/agt.2020.20.817

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

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