Redshift conjecture explained

K(R) 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 E _{infty} -ring spectra, after Hahn and Wilson did so earlier in the case of the truncated Brown-Peterson spectra BP\langle{n}\rangle .^[3]

References

Notes

• Ausoni . C. . Rognes . J. . The chromatic red-shift in algebraic K-theory . Enseign. Math. . 54 . 2 . 9–11 . 2008 .
• C. . Westerland . A higher chromatic analogue of the image of J . Geometry & Topology . 21 . 2 . 1033–93 . 2017 . 10.2140/gt.2017.21.1033 . 1210.2472. 44643197 .

• Burklund. Robert. Schlank. Tomer M.. Yuan. Allen. 2207.09929. The Chromatic Nullstellensatz . math.AT . 2022 .

Further reading

• Book: The Local Structure of Algebraic K-Theory . 18 . Algebra and Applications . Bjørn Ian . Dundas . Thomas G. . Goodwillie . Randy . McCarthy . . 2012 . 978-1447143932 . 313 (or 301).

Notes and References

1. Web site: Future directions . Tyler . Lawson . 2013 . Talbot 2013: Chromatic Homotopy Theory . MIT Talbot Workshop .
2. Web site: Algebraic K-theory of finitely presented ring spectra . John . Rognes . 2000 . Oberwolfach talk .
3. Burklund, Schlank, Yuan (2022). The Chromatic Nullstellensatz