Seminar

The Redshift Conjecture roughly says that the algebraic K-theory K(A) sees one more chromatic layer than the input A does.  Its spectacular start was the Lichtenbaum-Quillen conjecture, but through work of Madsen, Hesselholt, Rognes, Ausoni and many others, the conjecture has since then assumed an independent lifestyle, pretending to shed light on the increasingly complex module theory over ring spectra .

Most evidence for Redshift comes through a comparison via the trace and an analysis of the equivariant structure of smash powers of A.

So, one might reasonably ask whether this is the real foundation of the phenomenon and that Redshift for K-theory is just collateral.

I will try to illustrate the limit of our knowledge by asking open questions, both from calculational and more conceptual points of view.

Why does the group actions on smash product pair up precisely to build extensions giving redshift in the calculations?

Although the equivariant structure of smash powers is not a systematic theory parallel to the algebraic deformations lifting from finite to infinite characteristic and involving Witt rings/formal groups, does it tell us how to build one so that we really can talk systematically about redshift?

Essentially, I'll tell you about the stuff I can't do and invite you to play.