The Bousfield-Kuhn functor and topological Andre-Quillen cohomology

• 成果类型: Article
• 署名作者: Behrens, Mark; Rezk, Charles
• 署名单位: University of Notre Dame; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00941-x
• 发表日期: 2020
• 页码: 949-1022
• 关键词: power operations; Homotopy; HOMOLOGY; localization; SPECTRA; MODEL

摘要

We construct a natural transformation from the Bousfield-Kuhn functor evaluated on a space to the Topological Andre-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 v(n)-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.