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Redshift conjecture

From Wikipedia, the free encyclopedia

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.[1] 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.[2] In July 2022, Robert Burklund, Tomer Schlank and Allen 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 .[3]


References

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  1. ^ Lawson, Tyler (2013). "Future directions" (PDF). Talbot 2013: Chromatic Homotopy Theory. MIT Talbot Workshop.
  2. ^ Rognes, John (2000). "Algebraic K-theory of finitely presented ring spectra" (PDF). Oberwolfach talk.
  3. ^ Burklund, Schlank, Yuan (2022). The Chromatic Nullstellensatz
Notes
  • Burklund, Robert; Schlank, Tomer M.; Yuan, Allen (2022). "The Chromatic Nullstellensatz". arXiv:2207.09929 [math.AT].

Further reading

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