In mathematics, more specifically in chromatic homotopy theory, the redshift conjecture states, roughly, that algebraic K-theory K ( R ) {\displaystyle K(R)} has chromatic level one higher than that of a complex-oriented ring spectrum R. It was formulated by John Rognes in a lecture at Schloss Ringberg, Germany, in January 1999, and made more precise by him in a lecture at the Oberwolfach Research Institute for Mathematics, Germany, in September 2000. In July 2022, Robert Burklund, Tomer Schlank and Allen Yuan announced a solution of a version of the redshift conjecture for arbitrary E ∞ {\displaystyle E_{\infty }} -ring spectra, after Hahn and Wilson did so earlier in the case of the truncated Brown-Peterson spectra B P ⟨ n ⟩ {\displaystyle BP\langle {n}\rangle } .
References
Notes
Burklund, Robert; Schlank, Tomer M.; Yuan, Allen (2022). "The Chromatic Nullstellensatz". arXiv:2207.09929 [math.AT].
Further reading Dundas, Bjørn Ian; Goodwillie, Thomas G.; McCarthy, Randy (2012). The Local Structure of Algebraic K-Theory (PDF). Algebra and Applications. Vol. 18. Springer-Verlag. p. 313 (or 301). ISBN 978-1447143932. Archived from the original (PDF) on November 7, 2013.
External links red-shift conjecture at the nLab