Redshift conjecture

In mathematics, more specifically in chromatic homotopy theory, the redshift conjecture states, roughly, that algebraic K-theory $$K(R)$$ 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 Mathematische Forschungsinstitut Oberwolfach, 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 $$E_{\infty}$$-ring spectra, after Hahn and Wilson did so earlier in the case of the truncated Brown-Peterson spectra $$BP\langle{n}\rangle$$.