Redshift conjecture
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 } .