Wilson spaces, snaith constructions, and elliptic orientations
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222_2024_1239_ReferencePDF.pdf
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Author(s)
Chatham, Hood
Hahn, Jeremy
Yuan, Allen
Date Issued
February 15, 2024
Journal
Inventiones mathematicae
Publisher
Springer Berlin Heidelberg
Citation
Chatham, H., Hahn, J. & Yuan, A. Wilson spaces, snaith constructions, and elliptic orientations. Invent. math. 236, 165–217 (2024).
Version
Author's final manuscript
Abstract
We construct a canonical family of even periodic E ∞ -ring spectra, with exactly one member of the family for every prime p and chromatic height n . At height 1 our construction is due to Snaith, who built complex K -theory from CP ∞ . At height 2 we replace CP ∞ with a p -local retract of BU ⟨ 6 ⟩ , producing a new theory that orients elliptic, but not generic, height 2 Morava E -theories. In general our construction exhibits a kind of redshift, whereby BP ⟨ n − 1 ⟩ is used to produce a height n theory. A familiar sequence of Bocksteins, studied by Tamanoi, Ravenel, Wilson, and Yagita, relates the K ( n ) -localization of our height n ring to work of Peterson and Westerland building E n h S G ± from K ( Z , n + 1 ) .
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-ShareAlike
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DOI of Published Version
https://doi.org/10.1007/s00222-024-01239-3
