The Bousfield-Kuhn functor and topological André-Quillen cohomology

Mark Behrens, Charles Rezk

Research output: Contribution to journalArticlepeer-review


We construct a natural transformation from the Bousfield-Kuhn functor evaluated on a space to the Topological André-Quillen cohomology of the K(n)-local Spanier–Whitehead dual of the space, and show that the map is an equivalence in the case where the space is a sphere. This results in a method for computing unstable vn-periodic homotopy groups of spheres from their Morava E-cohomology (as modules over the Dyer-Lashof algebra of Morava E-theory). We relate the resulting algebraic computations to the algebraic geometry of isogenies between Lubin–Tate formal groups.

Original languageEnglish (US)
Pages (from-to)949-1022
Number of pages74
JournalInventiones Mathematicae
Issue number3
StatePublished - Jun 1 2020

ASJC Scopus subject areas

  • General Mathematics


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