Real topological Hochschild homology

Emanuele Dotto, Kristian J. Moi, Irakli Patchkoria, Sune Precht Reeh

Research output: Contribution to journalArticlepeer-review

Abstract

This paper interprets Hesselholt and Madsen’s real topological Hochschild homology functor THR in terms of the multiplicative norm construction. We show that THR satisfies cofinality and Morita invariance, and that it is suitably multiplicative. We then calculate its geometric fixed points and its Mackey functor of components, and show a decomposition result for groupalgebras. Using these structural results we determine the homotopy type of THR(Fp) and show that its bigraded homotopy groups are polynomial on one generator over the bigraded homotopy groups of H Fp. We then calculate the homotopy type of THR(Z) away from the prime 2, and the homotopy ring of the geometric fixed-points spectrum Φ
Z/2 THR(Z).
Original languageEnglish
Pages (from-to)63-152
Number of pages90
JournalJournal of the European Mathematical Society
Volume23
Issue number1
Early online date8 Oct 2020
DOIs
Publication statusPublished - Jan 2021

Keywords

  • Hochschild homology
  • involution
  • ring spectra

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