In mathematics, more specifically in
chromatic homotopy theory, the redshift conjecture states, roughly, that
algebraic K-theory 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, Burklund, Schlank and Yuan announced a solution of a version of the redshift conjecture for arbitrary
-ring spectra, after Hahn and Wilson did so earlier in the case of the truncated Brown-Peterson spectra BP
.[Burklund, Schlank, Yuan (2022). ''The Chromatic Nullstellensatz'']
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Algebraic topology
Homotopy theory
Conjectures
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