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 EnhSG± from K(Z,n+1).
Original language | English (US) |
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Pages (from-to) | 165-217 |
Number of pages | 53 |
Journal | Inventiones Mathematicae |
Volume | 236 |
Issue number | 1 |
DOIs | |
State | Published - Apr 2024 |
Funding
We thank Craig Westerland for some very enlightening discussions, particularly regarding Sects. & . We also owe thanks to Eric Peterson, Piotr Pstrągowski, Doug Ravenel, Andrew Senger, and Steve Wilson, and to the anonymous referee for numerous clarifying and enlightening remarks. Most of all we thank Mike Hopkins, Jacob Lurie, and Haynes Miller, who served as the three authors’ three PhD advisors and endured countless conversations about this work over the last several years. Through the course of the work, the second author was supported by NSF Grant DMS-1803273, and the third author by NSF Grant DGE-1122374.
ASJC Scopus subject areas
- General Mathematics